Question

16. A quanta of light having energy E, has wavelength equal to 800 nm. Calculate the wavelength
of photon of light which corresponds to energy 5E.
[Ans. 160 nm)​

Answer 1

Given :-

Energy of light = E

Wavelength of light = λ = 800 nm

Energy of photon = 5E

Let wavelength of photon = λ'

5E = hc/λ'

5E = hc/λ' -----(1)

5hc/λ = hc/λ'

λ' = λ/5

λ' = 800/5

$\bold{λ' =\:160\:nm}$

Answer 2

Given :-

A quanta of light having energy E, has wavelength equal to 800 nm.

To Find :-

Wavelength

Solution :-

Let the wavelength of the proton be λ'

We know that

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

$\sf 5E = \dfrac{hc}{\lambda'}$

$\sf 5\times\dfrac{hc}{\lambda} = \dfrac{hc}{\lambda'}$

Cancel hc from both sides

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

$\sf\dfrac{800}{5} = \lambda'$

$\sf 160 = \lambda'$