Question

.What is the wavelength and frequency of a photon emitted by a transition of an electron from a n-2 orbit to a 1 orbit?

Answer 1

Answer:

The frequency is $2.46\times10^{15}\ Hz$

The wavelength is $1.21\times10^{-7}\ m$

Explanation:

Given that,

A photon emitted by a transition of an electron from a n-2 orbit to n-1 orbit.

We know that,

For hydrogen atom, energy emitted due to transition of electron between two states

We need to calculate the energy

Using formula of energy

$E=13.6(\dfrac{1}{n_{f}^2}-\dfrac{1}{n_{i}^2})$

Put the value into the formula

$E=13.6(\dfrac{1}{1^2}-\dfrac{1}{2^2})$

$E=13.6(\dfrac{1}{1}-\dfrac{1}{4})$

$E=10.2\ eV$

$E=10.2\times1.6\times10^{-19}\ J$

$E=1.632\times10^{-18}\ J$

We need to calculate the frequency

Using formula of frequency

$E=h\nu$

$\nu=\dfrac{E}{h}$

Put the value into the formula

$\nu=\dfrac{1.632\times10^{-18}}{6.63\times10^{-34}}$

$\nu=2.46\times10^{15}\ Hz$

We need to calculate the wavelength

Using formula of wavelength

$\lambda=c\nu$

Put the value into the formula

$\lambda=\dfrac{3\times10^{8}}{2.46\times10^{15}}$

$\nu=1.21\times10^{-7}\ m$

Hence, The frequency is $2.46\times10^{15}\ Hz$

The wavelength is $1.21\times10^{-7}\ m$