Question

A metal surface is illuminated by the photons of
energy 5 eV and 2.5 eV respectively. The ratio of
their wavelengths is
(1) 1:3
(2) 1:4
(3) 2:5
(4) 1:2

Answer 1

Answer:

4) 1:2

We know by de-Broglie equation

E= hc/lamda

Energy is inversely proportional to the wavelength

let E1= 5 eV. E2= 2.5 eV

therefore lamda1/ lamda2 = E2/E1

=2.5/ 5

=1/2

Answer 2

The ratio of wavelength is 1:2

(4) is correct option.

Explanation:

Given that,

Energy of  photon E 5 eV

Energy of photon E'=2.5 eV

We know that,

The energy of photon is

$E=\dfrac{hc}{\lambda}$

Here,

$E\propto\dfrac{1}{\lambda}$

The energy is inversely proportional to the wavelength

We need to calculate the ratio of wavelength

Using formula of energy

$\dfrac{E}{E'}=\dfrac{\lambda'}{\lambda}$

$\dfrac{E'}{E}=\dfrac{\lambda}{\lambda'}$

Put the value into the formula

$\dfrac{2.5}{5}=\dfrac{\lambda}{\lambda'}$

$\dfrac{\lambda}{\lambda'}=\dfrac{1}{2}$

Hence, The ratio of wavelength is 1:2

Learn more :

Topic : photon energy

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