Which of the following statements are correct, if the threshold frequency of caesium is 5.16 \times10^14 ~Hz ? A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs , the ammeter shows the presence of current. B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced. C. When a red light is used instead of the yellow light, the current produced is higher with respect to the yellow light. D. When a blue light is used, the ammeter shows the formation of current. E. When a white light is used. the ammeter shows formation of current. Choose the correct answer from the options given below:

Structure of Atom PYQ — JEE Main 2025 · 7 Apr · Shift 1 · Q14 with Solution

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Correct answer: C

Use the photoelectric condition

For photoelectric emission to occur,

\nu \ge \nu_0

where $\nu_0 = 5.16 \times 10^{14}\,\text{Hz}$ is the threshold frequency of cesium.

If incident light has frequency less than threshold, no electrons are emitted, so no current is detected.

Compare common visible-light frequencies with the threshold

Using

\nu = \frac{c}{\lambda}

with $c = 3 \times 10^8\,\text{m/s}$ .

Typical wavelengths:

Red light: $\lambda \approx 650$ to $700\,\text{nm}$
Yellow light: $\lambda \approx 580\,\text{nm}$
Blue light: $\lambda \approx 450\,\text{nm}$
White light: mixture of all visible frequencies

Now estimate frequencies:

Yellow light ( $\lambda \approx 580\,\text{nm}$ ):

\nu_y = \frac{3\times 10^8}{580\times 10^{-9}} \approx 5.17\times 10^{14}\,\text{Hz}

So,

\nu_y > \nu_0

Hence yellow light can eject electrons.

Red light ( $\lambda \approx 650\,\text{nm}$ ):

\nu_r = \frac{3\times 10^8}{650\times 10^{-9}} \approx 4.62\times 10^{14}\,\text{Hz}

So,

\nu_r < \nu_0

Hence red light cannot eject electrons.

Blue light ( $\lambda \approx 450\,\text{nm}$ ):

\nu_b = \frac{3\times 10^8}{450\times 10^{-9}} \approx 6.67\times 10^{14}\,\text{Hz}

So,

\nu_b > \nu_0

Hence blue light can eject electrons.

White light contains many frequencies, including blue/violet and also yellow. Since it contains frequencies greater than threshold, photoelectric emission occurs.

Check each statement

Statement A

When Cs is illuminated with yellow light, current is observed.

Since yellow light has frequency just above threshold, photoelectrons are emitted.

So A is correct.

Statement B

If brightness of yellow light is reduced, the ammeter current is reduced.

For light above threshold, photocurrent depends on intensity (brightness). Lower intensity means fewer emitted electrons per second, hence lower current.

So B is correct.

Statement C

If red light is used instead of yellow light, current produced is higher.

Red light has frequency below threshold, so no photoelectrons are emitted. Thus current is not higher; it is essentially zero.

So C is incorrect.

Statement D

If blue light is used, current is observed.

Blue light has frequency above threshold, so photoelectric emission occurs.

So D is correct.

Statement E

If white light is used, current is observed.

White light contains frequencies above threshold, so electrons are emitted.

So E is correct.

Correct set of statements

The correct statements are:

A,\ B,\ D,\ E

This corresponds to Option C.

Comparison with stored answer

Stored correct answer: C

My derived answer: C

So they agree.

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View written solutionFree

Correct answer: C

Use the photoelectric condition

For photoelectric emission to occur,

\nu \ge \nu_0

where $\nu_0 = 5.16 \times 10^{14}\,\text{Hz}$ is the threshold frequency of cesium.

If incident light has frequency less than threshold, no electrons are emitted, so no current is detected.

Compare common visible-light frequencies with the threshold

Using

\nu = \frac{c}{\lambda}

with $c = 3 \times 10^8\,\text{m/s}$ .

Typical wavelengths:

Red light: $\lambda \approx 650$ to $700\,\text{nm}$
Yellow light: $\lambda \approx 580\,\text{nm}$
Blue light: $\lambda \approx 450\,\text{nm}$
White light: mixture of all visible frequencies

Now estimate frequencies:

Yellow light ( $\lambda \approx 580\,\text{nm}$ ):

\nu_y = \frac{3\times 10^8}{580\times 10^{-9}} \approx 5.17\times 10^{14}\,\text{Hz}

So,

\nu_y > \nu_0

Hence yellow light can eject electrons.

Red light ( $\lambda \approx 650\,\text{nm}$ ):

\nu_r = \frac{3\times 10^8}{650\times 10^{-9}} \approx 4.62\times 10^{14}\,\text{Hz}

So,

\nu_r < \nu_0

Hence red light cannot eject electrons.

Blue light ( $\lambda \approx 450\,\text{nm}$ ):

\nu_b = \frac{3\times 10^8}{450\times 10^{-9}} \approx 6.67\times 10^{14}\,\text{Hz}

So,

\nu_b > \nu_0

Hence blue light can eject electrons.

White light contains many frequencies, including blue/violet and also yellow. Since it contains frequencies greater than threshold, photoelectric emission occurs.

Check each statement

Statement A

When Cs is illuminated with yellow light, current is observed.

Since yellow light has frequency just above threshold, photoelectrons are emitted.

So A is correct.

Statement B

If brightness of yellow light is reduced, the ammeter current is reduced.

For light above threshold, photocurrent depends on intensity (brightness). Lower intensity means fewer emitted electrons per second, hence lower current.

So B is correct.

Statement C

If red light is used instead of yellow light, current produced is higher.

Red light has frequency below threshold, so no photoelectrons are emitted. Thus current is not higher; it is essentially zero.

So C is incorrect.

Statement D

If blue light is used, current is observed.

Blue light has frequency above threshold, so photoelectric emission occurs.

So D is correct.

Statement E

If white light is used, current is observed.

White light contains frequencies above threshold, so electrons are emitted.

So E is correct.

Correct set of statements

The correct statements are:

A,\ B,\ D,\ E

This corresponds to Option C.

Comparison with stored answer

Stored correct answer: C

My derived answer: C

So they agree.

Structure of Atom question

Structure of Atom question

Statement A

Statement B

Statement C

Statement D

Statement E

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Structure of Atom question

Structure of Atom question

Statement A

Statement B

Statement C

Statement D

Statement E

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