Respuesta :
Answer:
The frequency is [tex]2.46\times10^{15}\ Hz[/tex]
The wavelength is [tex]1.21\times10^{-7}\ m[/tex]
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
[tex]E=13.6(\dfrac{1}{n_{f}^2}-\dfrac{1}{n_{i}^2})[/tex]
Put the value into the formula
[tex]E=13.6(\dfrac{1}{1^2}-\dfrac{1}{2^2})[/tex]
[tex]E=13.6(\dfrac{1}{1}-\dfrac{1}{4})[/tex]
[tex]E=10.2\ eV[/tex]
[tex]E=10.2\times1.6\times10^{-19}\ J[/tex]
[tex]E=1.632\times10^{-18}\ J[/tex]
We need to calculate the frequency
Using formula of frequency
[tex]E=h\nu[/tex]
[tex]\nu=\dfrac{E}{h}[/tex]
Put the value into the formula
[tex]\nu=\dfrac{1.632\times10^{-18}}{6.63\times10^{-34}}[/tex]
[tex]\nu=2.46\times10^{15}\ Hz[/tex]
We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda=c\nu[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{3\times10^{8}}{2.46\times10^{15}}[/tex]
[tex]\nu=1.21\times10^{-7}\ m[/tex]
Hence, The frequency is [tex]2.46\times10^{15}\ Hz[/tex]
The wavelength is [tex]1.21\times10^{-7}\ m[/tex]
