Question

Some of the wave lengths observed in the emission spectrum of neutral hydrogen gas are $912, 1026, 1216, 3646, 6563$ $\mathring{A}$. If broad band light is passing through neutral hydrogen gas at room temperature , then the wavelength that will not be absorbed strongly is

• A. $1026\,\mathring{A}$
• B. $1216\,\mathring{A}$
• C. $912\,\mathring{A}$
• D. $3646\,\mathring{A}$

Answer 1

Answer: (D)

Energy of a photon with wavelength $\lambda$ is
$E=\frac{12400\left(eV.\,\mathring{A}\right)}{\lambda\left(\mathring{A}\right)}$
Energies of wavelengths (of photons) observed in emission spectrum are
$E_{1}=\frac{12400}{912}=13.5\,eV$
$E_{2}=\frac{12400}{1026}=12.08\,eV$
$E_{3}=\frac{12400}{1216}=10.2\,eV$
$E_{4}=\frac{12400}{3646}=3.4\,eV$
When these radiations pass through neutral hydrogen gas at room temperature, as all of atoms are probably in their ground states, absorbed energy must be more than or equal to $10.2\, eV$.

So, $\lambda=3646\,\mathring{A}$ wavelength is not strongly absorbed by the given sample.