technician otes aqa as and a evel physics otes 3 pearson ducation ltd 2018 physics aqa as and a...

$: Technician otes AQA AS and A evel Physics otes 3 Pearson ducation Ltd 2018 Physics AQA AS and A Level Practical 2: Investigation of interference in Young’s slit experiment and diffraction$
PhysicsAQA AS and A LevelTechnician Notes

1 © Pearson Education Ltd 2018

Practical 1: Investigation into the variation of the frequency of stationary waves on a string with length, tension, and mass per unit length of the string

Objectives

● To carry out an investigation into standing waves

● To develop the skills to carry out further investigations

Safety ! Equipment

● There are no hazards associated with this experiment if rubber is used as the medium. If metal wire is used, safety glasses should be worn.

● Follow the usual electrical precautions for mains powered apparatus, including a visual inspection of the supply lead.

● bench pulley

● slotted masses and hanger

● metre ruler

● 2 m length of rubber ‘string’

● vibration generator connected to a signal generator

Background

In this practical, students investigate the effect of changing variables – length, tension, and mass per unit length – on a variety of resonant frequencies. They are asked to write detailed methods for testing each variable, which teachers may wish to check before starting.

Procedure

Follow these steps to find the resonant frequency of a rubber ‘string’.

1. Students set up the practical by attaching one end of the string to the vibration generator. The other end of the string is passed over the bench pulley and attached to the mass hanger.

2. Students add masses until the total mass is 100 g.

3. The signal generator is turned on to set the rubber string oscillating. Students move the generator to vary the oscillating length, until resonance is observed.

4. Students use a cathode ray oscilloscope (or another suitable method) to obtain an accurate value for the frequency of the signal generator.



Objective

To determine the wavelength of laser light using Young’s fringes

Safety ! Equipment

● Lasers should be Class 2 and have a maximum output of 1 mW. They present little risk in the laboratory, provided sensible precautions are taken to reduce the risk of accidentally shining the light into eyes.

● CLEAPSS Laboratory Handbook section 12.12 and publication PS52 are helpful.

● Follow the usual electrical precautions for mains-powered apparatus, including a visual inspection of the supply lead.

● laser

● slide with double slit ‘rulings’

● white screen

● paper

● mounting material

● metre ruler

● optional: vernier microscope

Procedure

Part A: Young’s ‘double slit’ interference experiment

1. Students set up a laser and double slit slide, as shown in Figure A. The light can be shone onto a wall rather than a screen, but the surface must be matt to prevent too much of the beam being reflected in one direction. The distance, D, between the double slit slide and the screen should be approximately 1 metre.

D

fringe patternfringe width w

screen or non-reflective surface

double slitseparation s

laser

Figure A: Experimental set-up

2. Students move the laser so that the light shines through the double slit slide. An interference pattern should be visible on the screen.

3. The fringe spacing, w, is measured by averaging over a large number of visible fringes. (Measure across several fringes and divide this measurement by the number of fringes.) The best way to do this is to attach a sheet of paper to the screen (or wall), mark fringes on it, then remove the paper and measure over a large number of fringes.

4. The distance, D, is now measured.

5. Steps 1 to 4 are repeated, varying the distance D.

6. Students will require the slit separation, s. This may be printed on the slide, or if not, they can use a travelling or vernier microscope to measure this distance.

Practical 2: Investigation of interference in Young’s slit experiment and diffraction by a diffraction grating

Technician Notes


PhysicsAQA AS and A Level

Practical 2: Investigation of interference in Young’s slit experiment and diffraction by a diffraction grating

Procedure continued

Part B: Diffraction grating

1. With the laser approximately 4 m away from a large wall, the diffraction grating is placed in front of the laser. The laser beam should pass through the grating at normal incidence and meet the wall perpendicularly.

2. The distance, D, is measured between the grating and the wall.

3. Students turn on the laser and identify the zero-order maximum (straight through the grating).

4. They measure the distance x from the zero-order maximum to the first-order maxima (the closest maxima either side of the zero-order maximum).

The mean of these two values is the maximum produced according to n = 1 using the equation nλ = d sin θ. (Remind students, if necessary, that d is the distance between slits in the diffraction grating.)

5. They should now measure the distance x for increasing orders.

6. The measured values of x and D are used to calculate θ using tan θ = xD for each maximum.



Objectives

To measure the acceleration due to gravity, g of an object falling freely and to consider the following alternative methods:

● object falling through a trap door

● object falling through a light gate

Safety ! Equipment

● Ensure security of any apparatus that might topple over. A G-clamp can assist here.

● Be aware of falling objects.

● Turn off the electromagnet when it is not in use, as it will get hot.

● metre ruler or tape measure with millimetre resolution

● iron sphere

● electronic timer

● electromagnet to retain iron sphere

● two light gates (optional)

● clamp and stand

● low voltage power supply

● trap door switch

Background

It is difficult to produce a free-falling object in a laboratory, because the object will experience air resistance as it falls. For an object to be truly free falling, there must be no other forces acting on it.

However, if the object is made of a suitably dense substance, and its speed is not disproportionate, it can be considered to be falling freely. This means the appropriate SUVAT equation can be used to calculate g.

Procedure

1. The equipment is set up as shown in Figure A. (Note: light gates may be used as an alternative method, as shown in the set-up diagram on the right below.)


switch

electromagnet

trap door

s

timer0:00

stand clamp

electromagnet

light gate

light gatecounterweight

pad

h

Alternative Method

Practical 3: Determination of g by a free-fall method

Technician Notes



Practical 3: Determination of g by a free-fall method

Procedure continued

2. The object is dropped from rest and time, t, for the sphere to fall to the trap door switch is recorded.

3. Step 2 is repeated twice more and the mean value of t calculated.

4. The height, h, from which the object falls is measured and recorded.

5. Students repeat steps 2–4, varying the height each time. Readings should be taken for a minimum of six different heights.

6. For each height, students calculate the range for t in their readings. Dividing this value by 2 will give the uncertainty in t, from which the percentage uncertainty in t can be calculated.



Objective

To determine the Young modulus of a material by a simple method

Safety ! Equipment

● Wear safety goggles.

● Place a tray of sand or newspapers below weights.

● Do not stand close to where the weights can drop.

● 32 swg steel wire

● 28 swg copper wire

● scale and vernier arrangement with integral clamps for the wires

● scale and marker

● micrometer screw gauge

● metre ruler

● masses and mass holders

● safety goggles

● tray of sand

Background

There are two methods that can be used to determine the Young modulus of a wire: one suspends the test wire from the ceiling (Part A), while the other requires the test wire to be stretched horizontally (Part B).

Students are asked to write a method for each procedure, including diagrams to show how the apparatus is used in each case. They then use the method selected by the teacher and technician to determine the Young modulus of a wire.

Technician notes have been provided for both the vertical method (Part A) and horizontal method (Part B), so that teachers and technicians can choose the method best suited to the equipment available.

Procedure

Part A: Vertical method

1. Students set up the apparatus as shown in the diagram. They should make sure that all the wire clamps are fully tightened (note that details of the wire clamps are not shown on this diagram).

2. Students use the metre ruler to measure the initial length of the test wire, L.

3. A 1 kg mass hanger is attached to each wire to ensure both wires are initially stretched taut, and an initial scale reading is taken, using the vernier scale.

4. Students add an additional mass, of either 0.5 or 1 kg, to the test wire and take the new scale reading. The extension of the wire can be calculated by subtracting the initial scale reading from this second reading. Note that more readings can be obtained using the lighter masses.

5. This process is repeated, adding an extra mass each time, up to a total mass of around 8 kg. Students should take a scale reading and calculate the extension each time a mass is added.

6. When the total mass has been reached, a single mass is removed, and a new reading taken.

7. Students continue to unload the wire, one mass at a time, taking the scale reading each time.

8. Students measure the diameter of the wire at several places using a micrometer screw gauge. This diameter is then used to calculate A, the cross-section of the wire.

9. The Young modulus for the material of the wire (steel) can be calculated using the gradient of the graph of mean extension, e, against load, mg, together with the standard equation given below:

Young modulus E = tensile stress ____________ tensile strain

= mg/A

______ e/L

= mgL

____ Ae

Consequently e = mg × L/EA

Young modulus E can be calculated from the gradient = L/EA.

Practical 4: Determination of the Young modulus by a simple method

Technician Notes




Procedure continued

test wire

vernier scale

main scale

comparison wire

beam or solid support

slotted masses

L




Objective

To determine the Young modulus of a material by a simple method

Safety ! Equipment

● Wear safety goggles.

● Place a tray of sand or newspapers below weights.

● Do not stand close to where the weights can drop.

● 32 swg copper wire

● bench pulley

● slotted masses and hanger

● two wooden blocks and clamp

● small piece of sticky label to mark position on wire

● 90° set square

● metre ruler

● safety goggles

● tray of sand

Procedure

Part B: Horizontal method

1. The bench pulley is fixed at the end of the bench as shown in the diagram. One end of the wire is trapped between the two wooden blocks and the blocks are secured to the bench approximately 3 m from the pulley. The wire is laid out so that it passes over the pulley and the slotted mass are attached to the hanger to the end. The diameter, d, of the wire is measured.

L

G-clamp

metre ruler ortraveling microscopewooden blocks

markerpulley

slottedmasses

test wire

Figure B: Experimental set-up

2. Students lay the metre ruler under the wire near the pulley and attach the sticky label to the wire, to act as a length marker. The length can be judged by looking vertically down over the edge of the paper onto the scale of the metre ruler. If required, remind students to use the set square to help them do this.

3. The length of wire, ΔL, is measured from the wooden blocks to the edge of the paper.

4. Students add masses to the hanger and record the position of the marker against the metre ruler, calculating the extension L for each mass added.

5. At higher loads, significant creep may be observed, indicating that the elastic limit has been exceeded.




Objectives

● To determine the resistivity of a wire using ρ = A × R __ l

● To develop the skills to carry out further investigations

Safety ! Equipment

● With a high current, the wire can get hot. Do not touch the wire while the power is switched on, and switch off the power if you smell burning.

● ammeter

● voltmeter

● power pack (low voltage variable dc)

● 22 swg constantan wire

● crocodile clips

● connecting leads

● metre ruler

● micrometer

Procedure

1. Students measure the diameter of the constantan wire using a micrometer. They should take measurements in at least three places and in different directions to work out the mean diameter, d, converting this value to metres.

2. The equipment is set up as shown in Figure A.

wire being testedcrocodile clipcrocodile clip

dc supply

l

V

A


3. The wire is taped to the metre ruler and one crocodile clip attached at 0.

4. Students measure the current, I, with the voltage, V, at 0.5 V when the other crocodile clip is touched to the wire at 0.1 m. The second crocodile clip should be removed as soon as the current has been measured: the short length of wire will get very hot. The circuit should be switched off between readings.

5. Students measure the current and voltage several times for this length of wire, then use their values of I and V to calculate the mean resistance, R, for this length of wire.

6. Steps 4–5 are repeated, placing the second crocodile clip at 0.1 m intervals up to 0.8 m. The voltage will need to be altered to try to keep the current around 0.5 A.

Practical 5: Determination of resistivity of a wire using a micrometer, ammeter and voltmeter



Objective

To make measurements using an electrical circuit

Safety ! Equipment

● Do NOT use rechargeable batteries, due to the risk of short circuit. See CLEAPSS guidance leaflet GL225 for advice on using batteries in general practical circuit work.

● Follow normal laboratory safety procedures.

● voltmeter on 2 V range

● ammeter on 200 mA range


● electrical cell such as a 1.5 V cell (avoid using brand new or very old cells)

● variable resistor

Procedure

1. The circuit is set up as shown in Figure A.

V

A

Figure A: Circuit diagram

2. For potential difference, V, on the voltmeter, readings should be taken with the switch open.

3. For subsequent readings of potential difference and current, I, the switch should be closed. However, students must keep the switch open when not recording values.

4. Students take a minimum of six readings at different values of resistance. Resistance is changed by altering the variable resistor. Potential difference and current should both be recorded.

Practical 6: Investigation of the emf and internal resistance of electric cells and batteries by measuring the variation of the terminal pd of the cell with current in it

PhysicsTechnician Notes


AQA A LevelPractical 7: Investigation into simple harmonic motion using a mass–spring system and a simple pendulum

Objectives

To investigate the factors affecting the time period of a simple pendulum

Safety ! Equipment

● If you provide students with optical pins, ask them to take care with the points.

● It is recommended to use a G-clamp to secure the retort stand and prevent it from tipping over.

● three pendulum bobs of different mass

● long string

● metre ruler

● retort stand with clamp and boss

● two small wooden blocks

● stop clock

● optical pins or similar

● adhesive putty

Procedure

Part A: Simple pendulum

1. The apparatus is set up as shown in Figure A. It is difficult to see from the diagram, but the pendulum bob string should be clamped between two small wooden blocks. The fiducial marker could also be a piece of card with a line drawn on it, attached to the stand behind the pendulum.

fiducial marker

length, l


2. The pendulum length, l, should be measured from the top of the bob to the point where it is attached to the clamp. The radius of the bob is then added to the first measurement to give the correct value of l.

3. The fiducial marker sits directly under the bob. This will mark the centre of each oscillation as the pendulum oscillates.

5. Once students have recorded the time for ten oscillations, they find the average time for one oscillation and record this as the time period, T.

6. Students repeat steps 4 and 5, extending the string in steps of 0.2 m, up to 1.0 m.

7. They then repeat steps 4 to 6 using two other pendulum bobs of different mass.



AQA A Level

Objective

To investigate the time period of a mass–spring system

Safety ! Equipment

● As this is a mass–spring system, use a G-clamp to prevent the retort stand tipping over.

● retort stand, boss and clamp

● helical spring

● selection of masses

● stop clock

Procedure

Part B: Mass–spring system

1. The apparatus is set up as shown in the diagram. The fiducial marker should be level with the bottom of the mass. This will become the centre of the oscillations.

fiducialmarker

mass

spring

clamp


2. Students hang a mass of 0.1 kg from the spring, then create a small displacement and time ten oscillations.

3. The time for one oscillation should be calculated from this result, and recorded as T.

4. Repeat steps 3 and 4 with 0.2 kg, 0.3 kg, 0.4 kg and 0.5 kg masses.

Practical 7: Investigation into simple harmonic motion using a mass–spring system and a simple pendulum



AQA A LevelPractical 8: Investigation of Boyle’s law (constant temperature) and Charles’s law (constant pressure) for a gas

Objective

To explore the relationship between pressure, volume and temperature for gases (Boyle’s law)

Safety ! Equipment

● Teachers should check that the sealed tube used in this practical is protected within a Perspex® tube.

● Boyle’s law apparatus

● Pump

Procedure

Part A: Boyle’s law

to foot pump

0

valve

pressuregauge

oil

trapped air102030405060708090

Figure A: Apparatus used to demonstrate the relationship between pressure and volume

1. Using the apparatus provided, students take a reading for the pressure on the gauge and a reading for the volume of air in the tube, recording the results in a suitable table.

2. Students use the pump to increase the pressure by approximately 10 kPa, then take the new pressure and volume readings.

3. Step 3 is then repeated for at least five more sets of readings, pausing between readings to let the gas cool down.

4. Students take another set of readings whilst reducing the pressure in steps of approximately 10 kPa.



AQA A Level

Objective

To estimate absolute zero

Safety ! Equipment

● Students must take care with the heated water, especially as the beaker will have tall objects in it.

● The capillary tube contains concentrated sulfuric acid or mercury (see CLEAPSS Hazcard HC062). This, plus the very hot water, means eye protection should be worn. CLEAPSS Guide R231 provides further guidance.

● beaker

● kettle

● 30 cm ruler

● capillary tube with plug of acid or mercury

● thermometer

● clamp

Procedure

Part B: Charles’s law

1. The apparatus is set up as shown in Figure A. Remember that the capillary tube contains a drop of concentrated sulfuric acid or mercury and must be handled with care. The capillary tube can be secured to the ruler using rubber bands.

capillary tube

elastic band

elastic bandheat-proof mat(to protect bench)

hot water

2 litre beaker

thermometer30 cm ruler

Figure A: Apparatus to test Charles’s law

2. Students measure and record the height of the column of air, h. This is measured from the bottom of the capillary tube to the drop of acid.

3. Water is boiled in a kettle. Students then allow the water to cool slightly before adding it to the beaker. Allowing the water to cool prevents the ruler from warping.

4. Students record both h and θ as the temperature decreases, stirring the water with the thermometer. They should try to take measurements roughly every 5 °C, until a constant temperature is reached.

Practical 8: Investigation of Boyle’s law (constant temperature) and Charles’s law (constant pressure) for a gas



AQA A Level

Objectives

● To discharge a capacitor through a resistor

● To charge a capacitor through a resistor

Safety ! Equipment

● Do not exceed the voltage rating of the capacitor. Voltage must be less than 40 V DC

● Take care to avoid any short circuits.

● Make sure electrolytic capacitors are connected the correct way around.

● voltmeter

● ammeter

● capacitors (suitable values: 4700 μF, 2200 μF, 1000 μF)

● resistors

● battery (1.5 V or half the voltage rating of the capacitor)

● SPDT switch


● stop clock

Procedure

Part A: Discharging

1. The circuit is set up as shown in Figure A.

A B

C +– V R

Figure A: Circuit set-up

2. To charge the capacitor, the two-pole switch is set to position A. The charging current is usually at a safe value, because it is limited by the internal resistance of the battery. However, the capacitor will charge up almost instantly.

3. The switch is moved to position B to discharge the capacitor, C, through the resistor, R. Use this procedure to check that all components are working as expected.

4. With the capacitor charged, the switch is moved to position B. The stop clock is started at the same time. Students record the initial voltage reading at time zero (t = 0), then take further readings at 5-second intervals as the capacitor discharges.

5. Step 4 is repeated with different resistors. There is also scope for students to repeat the procedure with different capacitors, depending on time and capacitor availability.

Practical 9: Investigation of the charge and discharge of capacitors

Technician Notes


PhysicsAQA A Level

Practical 9: Investigation of the charge and discharge of capacitors

Procedure continued

Part B: Charging

1. The circuit is set up as shown in Figure B. The voltmeter should read zero with the capacitor uncharged.

+–

R

C V

Figure B: Circuit set-up

2. The capacitor is charged by closing the switch. Students record the voltage at 5-second intervals as the capacitor charges.

3. Step 2 is repeated using different resistors and capacitors.



AQA A Level

Objective

To investigate the relationship between force, magnetic flux density, current and length

Safety ! Equipment

● Take care, as the equipment may become warm.

● Turn off the circuit between readings.

● power supply (low voltage DC)

● ammeter

● thick copper wire

● clamp stands

● crocodile clips


● four magnadur magnets with a metal cradle

● electronic top pan balance

● 30 cm ruler

Background

The force F (N) acting on a wire of length L (m), with a current I (A) passing through it, in a magnetic field with flux density B (T) at an angle θ to the field is given by: F = BIL sin θ.

The force on the wire will have its maximum value when the wire is perpendicular to the field lines.

At this point, θ = 90°, so and the force on the wire, F = BIL.

Procedure

1. Students set up the equipment as shown in Figure A. This is quite a complicated set-up, so teachers may wish to prepare a set-up in advance, to act as a model for students to follow.

a magnadur magnetsin metal cradle

copper wire(clamped at each end)

two magnets oneither side

electronic balance

N S

c

l

magnadur magnetsin cradle

+ –

crocodile clip

current

S

N

0–6V dc

clamp on stand

A

Figure A: (a) End view, (b) side view and (c) top view

b

magnadur magnetsin cradle placed on electronic balance

currentSN

lcopper wire

downward forceon cradle

Practical 10: Investigation into how the force on a wire varies with flux density, current and length of wire using a top pan balance

Technician Notes


AQA A Level

PhysicsPractical 10: Investigation into how the force on a wire varies with flux density, current and length of wire using a top pan balance

Procedure continued

2. With no current flowing in the circuit, the balance is zeroed.

3. The voltage on the power supply is increased to obtain a current, I, of 6.0 A (as read from the ammeter). This should be treated as a maximum.

4. The value on the balance, m, is recorded in grams.

5. Repeat steps 3 and 4 to obtain values for I at 1 A intervals from 5.0 A to 1.0 A.

6. Students repeat the whole experiment, to obtain a second set of results, which are then used to calculate a mean value of m for each value of I.



AQA A Level

Objective

To investigate the relationship between magnetic flux linkage and angle

Safety ! Equipment

● Take care, as the equipment may become warm.

● Turn off the circuit between readings.

● oscilloscope

● power supply (low voltage AC)

● large circular coil and stand


● protractor

● search coil and stand

Background

Flux linkage can be calculated using the equation:

BAN cos θ = flux linkage

where N is the number of turns in a coil of area A with its axis at an angle θ to a magnetic field of strength B.

In the set-up shown in Figure A, the search coil is clamped so that the plane of the coil is parallel to the plane of the large circular coil, and perpendicular to the field lines produced by the circular coil. This will produce the maximum induced emf in the search coil and the maximum flux linkage with cos θ = 1.

Note that a large protractor clamped behind the search coil support rod can help in measuring the angle of the search coil.

Procedure

Test A

1. Students set up the equipment as shown in Figure A. Teachers may wish to prepare a set-up in advance, as a model for students to follow while setting up their own equipment.

circular coil

search coil

50 Hz AC lowvoltage supply orAF signal generator

cathode rayoscilloscope


2. To begin, the time base on the oscilloscope is switched off, so that the induced emf is displayed as a vertical line.

3. Students measure the length of the vertical line and divide by two to calculate the amplitude of the induced emf. (Refer to the y-gain setting on the oscilloscope.)

4. Altering the angle of the search coil (the angle between the plane of the circular coil and the plane of the search coil) will alter the value of the induced emf. Students record the angle of the search coil and the peak value of the induced emf.

5. Step 4 is repeated for at least ten different angles. If there is time, students should try to take measurements every 20°.

Practical 11: Investigation, using a search coil and oscilloscope, of the effect on magnetic flux linkage of varying the angle between a search coil and magnetic field direction



AQA A Level

Objective

To investigate the inverse-square law for gamma rays

Safety ! Equipment

● This practical involves a radiation hazard and important rules must be followed. CLEAPSS Guide L93 provides more information.

● Students must follow instructions carefully.

● Gamma sources must only be handled using tongs, with the active end pointing away from any people, including the person handling.

● Geiger–Müller tube

● scalar counter

● metre ruler

● stop clock

● sealed gamma source (e.g. cobalt 60 or caesium 137)

● tongs for handling the gamma source

Procedure

GM tube

gamma source

metre ruler

stop clock

scaler

d


1. With the gamma source in the box, the Geiger–Müller tube is placed on the bench and plugged it into the scaler. Start the scaler to check that it is working.

2. With the gamma source still in its box (and as far away from the apparatus as possible), the background radiation, C0, is measured. The scaler should be switched on and a stop clock started at the same time. After 20 minutes, the total counts, N, on the scaler and the time, t are recorded.

3. The apparatus is set up as shown in Figure A, with the source in its holder (not shown in the diagram). Make sure that students follow all relevant safety procedures when handing the source.

4. Students take some preliminary readings to establish the maximum distance, x, at which the count is above the background value.

5. The Geiger–Müller tube should be placed 0.70 m from the source (d = 0.70 m) – assuming this gives a count rate above background. If not, the detector should be moved closer to the source.

6. Students switch on the scaler and start the stop clock at the same time. Record the count, N, after 100 s (t). Repeat two more times and work out the average count rate, C.

7. Repeat steps 5 and 6, moving the Geiger–Müller tube towards the source in 0.10 m steps until x = 0.10 m.

8. Subtract the background count (C0) from the average count rate (C) to obtain the corrected count rate (Cc).

9. Record N, t, x in a suitable table, including columns for count rate C = N __ t , corrected count rate Cc and 1 ___

√ __

Cc .

Practical 12: Investigation of the inverse-square law for gamma radiation

Published by Pearson Education Limited, 80 Strand, London, WC2R 0RL.

www.pearsonschoolsandfecolleges.co.uk

Text © Pearson Education Limited 2018

Typeset and illustrated by Tech-Set Ltd Gateshead

Original illustrations © Pearson Education Limited

First published 2018

Copyright notice

All rights reserved. The material in this publication is copyright. Activity sheets may be freely photocopied for classroom use in the purchasing institution. However, this material is copyright and under no circumstances may copies be offered for sale. If you wish to use the material in any way other than that specified you must apply in writing to the publishers.

Acknowledgements

The publishers would like to thank John Kavanagh for his contributions to the text.

Note from the publisher

Pearson has robust editorial processes, including answer and fact checks, to ensure the accuracy of the content in this publication, and every effort is made to ensure this publication is free of errors. We are, however, only human, and occasionally errors do occur. Pearson is not liable for any misunderstandings that arise as a result of errors in this publication, but it is our priority to ensure that the content is accurate. If you spot an error, please do contact us at [email protected] so we can make sure it is corrected.


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