Question 114: Atoms & Nuclei

Question

A hydrogen atom in its ground state is irradiated by light of wavelength 970$$\mathop A\limits^o $$.Taking hc  = 1.237 $$	imes$$ 10$$-$$6 eVm and the ground state energy of hydrogen atom as $$-$$ 13.6 eV, the number of lines present in the emission spectrum is

Accepted Answer

The energy of the incident photon of wavelength $\lambda=970 $ $$\mathop A\limits^o $$ is
$$
\Delta E=\frac{h c}{\lambda}=\frac{1.237 	imes 10^{-6}}{970 	imes 10^{-10}}=12.75 \mathrm{eV}
$$
$$
\begin{aligned}
& 	ext { Final energy of electron in } n^{	ext {th }} 	ext { state }=-\frac{13.6}{n^2} \mathrm{eV} \\
& \Rightarrow-\frac{13.6}{n^2}=-13.6+12.75=-0.85 \\
& \Rightarrow n^2=16 \Rightarrow n=4
\end{aligned}
$$
The hydrogen atom can make ${ }^n \mathrm{C}_2=6$ transitions while returning to ground state. Thus, the emission spectrum will have six lines.

Atoms & Nuclei

A hydrogen atom in its ground state is irradiated by light of wavelength 970$\mathop A\limits^o .Taking hc = 1.237 \times 10-6 eVm and the ground state energy of hydrogen atom as -$ 13.6 eV, the number of lines present in the emission spectrum is

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