Question

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the $n=4$ level. Determine the wavelength and frequency of photon.

• A. $9.7\times 10^{-8}m$ and $3.1\times 10^{15}Hz$
• B. $7.6\times 10^{-9}m$ and $2.6\times 10^{14}Hz$
• C. $2.9\times 10^{-10}m$ and $4.9\times 10^{12}Hz$
• D. $8.6\times 10^{-9}m$ and $3.1\times 10^{14}Hz$

Answer 1

Answer: (A)

For ground state $n_1=1$ to $n_2=4$
Energy absorbed by photon : $E=E_2-E_1$
$=+13.6\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)\times 1.6\times 10^{-16}J$
$=13.6\left(\frac{1}{1}-\frac{1}{4^2}\right)\times 1.6\times 10^{-19}$
$=13.6\times 1.6\times 10^{-19}\left(\frac{15}{16}\right)$
$=20.4\times 10^{-19}$
or $E=h\nu =20.4\times 10^{-19}$
Frequency $\nu =\frac{20.4\times 10^{-19}}{h}=\frac{20.4\times 10^{-19}}{6.63\times 10^{-34}}$
$=3.076\times 10^{15}$
$=3.1\times 10^{15}Hz$
Wavelength of photon $\lambda =\frac{c}{\nu }$
$=\frac{3\times 10^8}{3.076\times 10^{15}}$
$=9.74\times 10^{-8}m$
Thus, the wavelength is $9.7\times 10^{-8}m$ and frequency is $3.1\times 10^{15}Hz$