Question

Question: For the H atom, the transition from the 2p state to the 1s state is accompanied by the emission of a photon with an energy of$16.2\times {10}^{-19}\mathrm{J}$. For an Fe atom, the same transition (2p to 1s) is accompanied by the emission of X-rays of 0.193-nm wavelengths. What is the energy difference between these states in iron? Comment on the reason for the variation (if any) in the 2p-1s energy-level spacing for these two atoms.

Short answer

The energy emitted by Fe atom is $1.029\times {10}^{-15}\mathrm{J}$.The energy emitted by H atom is greater than that of Fe-atom.

Step-by-step solution

Step 1:

According to the question,

For H atom,$\mathrm{E}=16.2\times {10}^{-19}\mathrm{J}$

For Fe atom,$\mathrm{\lambda }=0.193\mathrm{nm}=0.193\times {10}^{-9}\mathrm{m}$

So, according to energy of electro-magnetic wave,

$$\begin{gathered} \mathrm{E}=\frac{\mathrm{hc}}{\mathrm{\lambda }} \\ =\frac{6.623\times {10}^{-34}\times 3\times {10}^8}{0.193\times {10}^{-9}}\mathrm{J} \\ =\frac{19.862\times {10}^{26}}{0.193\times {10}^{-9}}\mathrm{J} \\ =102.95\times {10}^{-17}\mathrm{J} \\ =1.029\times {10}^{-15}\mathrm{J} \end{gathered}$$

So the energy emitted by Fe atom is $1.029\times {10}^{-15}\mathrm{J}$.

Step 2:

The energy emitted by H atom is greater than that of Fe-atom.