Question

When a photon of suitable frequency is incident on a metal surface, photoelectron is emitted from it. If the frequency is below a threshold frequency (vo) for the surface, no photoelectron is emitted. For a photon of frequency v(v > vo), the kinetic energy of the emitted photoelectrons is h(v − vo). The photocurrent can be stopped by applying a potential Vo called ‘stopping potential’ on the anode. Thus maximum kinetic energy of photoelectrons Km = eVo = h(v − vo). The experimental graph between Vo and v for a metal is shown in figure. This is a straight line of slope m.

(i) The straight line graphs obtained for two metals ______.

1. coincide each other.
2. are parallel to each other.
3. are not parallel to each other and cross at a point on v-axis.
4. are not parallel to each other and do not cross at a point on v-axis.

(ii) The value of Planck’s constant for this metal is ______.

1. `e/m`
2. `1/(me)`
3. me
4. `m/e`

(iii) The intercepts on v-axis and V_o-axis of the graph are respectively ______.

1. v_o, `(hv_o)/e`
2. v_o, hv_o
3. `(hv_o)/e`, v_o
4. hv_o, v_o

OR

(iii) When the wavelength of a photon is doubled, how many times its wave number and frequency become, respectively?

1. 2, `1/2`
2. `1/2, 1/2`
3. `1/2`, 2
4. 2, 2

(iv) The momentum of a photon is 5.0 × 10⁻²⁹ kg. m/s. Ignoring relativistic effects (if any), the wavelength of the photon is ______.

1. 1.33 μm
2. 3.3 μm
3. 16.6 μm
4. 13.3 μm

Answer 1

(i) The straight line graphs obtained for two metals are parallel to each other.

Explanation:

If two metals have different work functions, their straight line graphs are parallel to each other

(ii) The value of Planck’s constant for this metal is me.

Explanation:

From the graph: 

Slope (m) = `h/e`

Then, h = e.m

(iii) The intercepts on v-axis and V_o-axis of the graph are respectively `bbunderline(v_o, (hv_o)/e)`.

Explanation:

From the graph, the intercept on the v-axis is v_o, and the intercept on the v_o-axis is hv_o/e.

So, `(v_o, (hv_o)/e)`

OR

`bb(1/2, 1/2)`

Explanation:

Wave number (k) i = `(2 pi)/lambda`

When λ is doubled, k becomes half.

Frequency (f) = `c/lambda`

When λ is doubled, f becomes half.

So, `(1/2, 1/2)`

(iv) The momentum of a photon is 5.0 × 10⁻²⁹ kg. m/s. Ignoring relativistic effects (if any), the wavelength of the photon is 13.3 μm.

Explanation:

Given: ρ = `h/lambda`

λ = `h/p`

= `(6.63 xx 10^-34)/(5.0 xx 10^-29)`

= 1.33  × 10⁻⁵ m

= 1.33 μm