Question

The wavelength of a photon is Angstrom units having energy of one electron volt is:
a.) $2.42\times {{10}^{3}}{{A}^{o}}$
b.) $3.42\times {{10}^{3}}{{A}^{o}}$
c.) $2.42\times {{10}^{4}}{{A}^{o}}$
d.) None of these

Answer 1

Hint: The relation for energy and wavelength is $E = \dfrac{hc}{\lambda }$. Use this relation to find out the different wavelengths corresponding to the different energies. Try to convert the units of energy from electron volts to meters and Angstrom units using certain constants in their relation.

Complete Solution :
We know that the formula for the energy is $E=h\nu $
Where $E$ = energy
$h$ = planck's constant
$\nu $ = frequency
Also the relation between the wavelength and frequency is $\nu =\dfrac{c}{\lambda }$
Where $c$ = speed of light in vacuum
$\lambda $ = wavelength

Therefore the relation between the energy and the wavelength is defined as
$E =\dfrac{hc}{\lambda }$
Given the energy is $1ev$
We know that $1ev$ is equal to $1.6\times {{10}^{-19}}J$
The value of the speed of light in vacuum is $c = 3\times {{10}^{8}}m/s$
The value of the planck's constant is $h = 6.6\times {{10}^{36}}Js$
Put all the given values in the above equation and calculate the wavelength corresponds to the energy of $1ev$

$1.6\times {{10}^{-19}}=\dfrac{6.6\times {{10}^{36}}\times 3\times {{10}^{8}}}{\lambda }$
After simplifying the above equation we obtained the value of the wavelength corresponds to the energy of $1ev$ is

$\lambda = 1.24\times {{10}^{-8}}m$
Therefore the required value of the wavelength corresponds to the given energy is $\lambda =124{{A}^{o}}$
So, the correct answer is “Option D”.

Note: While converting the units from one system to another system we need to take care that the system is balanced. For example if we multiplied the answer by 0.001 to convert the units from one system to the other then to balance the answer and not to obtain any error values we should multiply it by multiplying by 1000.