Question 32: Atoms & Nuclei

Question

Which, of the following is true of the Balmer series of the hydrogen spectrum?
a. The series is in the visible region.
b. The entire series falls in the ultraviolet region
c. The entire series falls in the infrared region
d. The series is partly in the visible region and partly in the infrared region

Accepted Answer

BalmerÃ¢ÂÂformula for hydrogen transitions to level $n=2$:
$$\frac{1}{\lambda} \;=\; R_H\Bigl(\frac{1}{2^2}-\frac{1}{n^2}\Bigr)\quad(n=3,4,5,\dots)$$
where $R_H$ is the Rydberg constant (Ã¢ÂÂ 1.097ÃÂ10^7 mÃ¢ÂÂ»ÃÂ¹).
Calculated wavelengths:
$n=3	o2$ (HÃÂ±): 656.3 nm
$n=4	o2$ (HÃÂ²): 486.1 nm
$n=5	o2$ (HÃÂ³): 434.0 nm
$n=6	o2$ (HÃÂ´): 410.2 nm
Ã¢ÂÂ¦ converging to 364.6 nm as $n	o\infty$.
Visible spectrum spans roughly 380Ã¢ÂÂ750 nm. All principal Balmer lines lie between 364.6 nm and 656.3 nm, with the strongest (HÃÂ± to HÃÂ´) well inside 400Ã¢ÂÂ700 nm.
Conclusion: the Balmer series is observed in the visible region.
Answer choice: (a).

Answer

b

Answer

c

Answer

a

Answer

d

Atoms & Nuclei

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