Question

A hydrogen atom in the ground state absorbs a photon of wavelength 95.0 nm.
What energy level does the electron reach?

Answer 1

I know the answer's 5. But can someone show me the calculations?

Answer 2

\[E=\frac{ hc }{ \lambda }\]

Answer 3

Ground energy Level of Hydrogen is -13.2eV

Answer 4

Wavelength given is \(95.0 nm=95.0 \times 10^{-9}m\)
\[\lambda=95 \times 10^{-9} \\ \\ E=\frac{hc}{\lambda} \\ \\ E=\frac{(6.63\times 10^{-34})(3 \times 10^8)}{(95\times 10^{-9})} \\ \\E=2.094 \times 10^{-18}J \\ \\ \text{For each energy level,} \\ \\ \frac{2.094\times 10^{-18}}{e}=13.1eV\]
13.1 Which is the fifth energy level.

Answer 5

\[E=\frac{ 2.18*10^-18 Z^2 }{ n^2 }\]

Answer 6

Use the rydberg equation:

\[\frac{ 1 }{ \lambda} = R (\frac{1}{n _{1}^{2} }- \frac{ 1 }{ n _{2}^{2} })\]

\[\frac{ 1 }{ 9.5x10^-8} = 1.097x10^7 (\frac{1}{1^{2} }- \frac{ 1 }{ n _{2}^{2} })\]

isolate \[n _{2}\]

Answer 7

ps. i messed up the order of the n's
it should read:
\[(\frac{ 1 }{ n _{f}^{2} }-\frac{ 1 }{ n _{i}^{2} })\]

i= initial, f= final

\[(\frac{ 1 }{ n _{f}^{2} }-\frac{1}{1^{2} })\]