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

The frequency is
`2.46*10^(15)\ Hz`

The wavelength is
`1.21*10^(-7)\ m`

Step-by-step 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((1)/(n_(f)^2)-(1)/(n_(i)^2))`

Put the value into the formula

`E=13.6((1)/(1^2)-(1)/(2^2))`

`E=13.6((1)/(1)-(1)/(4))`

`E=10.2\ eV`

`E=10.2*1.6*10^(-19)\ J`

`E=1.632*10^(-18)\ J`

We need to calculate the frequency

Using formula of frequency

`E=h\\u`

`\\u=(E)/(h)`

Put the value into the formula

`\\u=(1.632*10^(-18))/(6.63*10^(-34))`

`\\u=2.46*10^(15)\ Hz`

We need to calculate the wavelength

Using formula of wavelength

`\lambda=c\\u`

Put the value into the formula

`\lambda=(3*10^(8))/(2.46*10^(15))`

`\\u=1.21*10^(-7)\ m`

Hence, The frequency is
`2.46*10^(15)\ Hz`

The wavelength is
`1.21*10^(-7)\ m`