Question

In an experiment, a student found that a maximum wavelength of 351 nm is needed to just dislodge electrons from a metal surface. calculate the velocity (in m/s) of an ejected electron when the student employed light with a wavelength of 313 nm.

Answer 1

`v = 3.94 * 10^5 m/s`

Step-by-step explanation:

As we know that the maximum wavelength needed to remove the electron from metal surface is given as

`\lambda = 351 nm`

so we have work function of metal is given as

`\phi = (hc)/(\lambda)`

`\phi = (1240)/(351) eV`

`\phi = 3.53 eV`

Now as per Einstein's equation for photo electric effect we know that

`E = \phi + (1)/(2)mv^2`

`(hc)/(\lambda) = \phi + (1)/(2)mv^2`

`((1240)/(313) - 3.52)1.6 * 10^(-19) = (1)/(2)(9.1* 10^(-31))v^2`

`7.07 * 10^(-20) = (1)/(2)(9.1* 10^(-31))v^2`

`v = 3.94 * 10^5 m/s`

Answer 2

Before solving this question first we have to understand work function.

The work function of a metal is amount of minimum energy required to emit an electron from the surface barrier of metal . Whenever the metal will be exposed to radiation a part of its energy will be utilized to emit an electron while rest will provide kinetic energy to the electron.

Let f is the frequency of incident radiation and f' is the frequency corresponding to work function. Let v is the velocity of the ejected electron.

we know that velocity of an electromagnetic wave is the product of frequency and wavelength. Hence frequency f is given as-

`f=(c)/(\lambda)`

where c is velocity of light and
`\lambda` is the wavelength of the wave.

As per the question incident wavelength =313 nm

`313*10^(-9) m` [as 1 nm =10^-9 m]

The wavelength corresponding to work function is 351 nm i.e

`351*10^(-9) m`

we know that hf=hf'+K.E [ h is the planck's constant whose value is 6.63×10^-34 J-s]

⇒K.E =hf-hf'

`(1)/(2) mv^2=hf-hf'`

`v^2=(2)/(m) [hf-hf']`

`v^2=(2)/(m) [(hc)/(\lambda) -(hc)/(\lambda ' )]`

`=(2)/(9.1*10^(-31)kg ) *{6.63*10^(-34) Js *3*10^(8) [(1)/(313*10^(-9) ) -(1)/(351*10^(-9) ) ]`

`=0.001512021301356*10^(14) m^2/s^2`

`v=\sqrt{0.0015120241301356*10^(14) } m/s`

`=0.3888476161313*10^(7) m/s`

`=3.88848*10^(7) m/s` [ans]