Question

The number of spectral lines that are possible when electrons in the $7^{\mathrm{th}}$ shell of different hydrogen atoms return to the $2^{\mathrm{nd}}$ shell is:

• A. $12$
• B. $15$
• C. $14$
• D. $10$

Answer 1

The correct option is B

$15$

Explanation for the correct option:

[B]$15$

• Spectral line is a confined spectrum in which a certain wavelength of light is emitted or absorbed.
• No. of spectral lines$=\left\{\right[{\mathrm{n}}_2-{\mathrm{n}}_1\left]\right[{\mathrm{n}}_2-{\mathrm{n}}_1+1\left]\right\}$$/2$
• Where, ${\mathrm{n}}_2=$ Higher Energy level
• So, ${\mathrm{n}}_2=$$7$
• And, ${\mathrm{n}}_1=$Lower Energy level
• So,${\mathrm{n}}_1=$$2$
• So, No. of spectral lines$=\left\{\right[7-2\left]\right[7-2+1\left]\right\}$$/2$
• No. of spectral lines$=15$

So, option [B] is correct.

Explanation for the Incorrect options:

[A]$12$

• No. of spectral lines$=\left\{\right[{\mathrm{n}}_2-{\mathrm{n}}_1\left]\right[{\mathrm{n}}_2-{\mathrm{n}}_1+1\left]\right\}$$/2$
• Where, ${\mathrm{n}}_1=$$2$
• And, ${\mathrm{n}}_2=$$7$
• So, No. of spectral lines$=15$.

So, option[A] is incorrect.

[C]$14$

• No. of spectral lines$=\left\{\right[{\mathrm{n}}_2-{\mathrm{n}}_1\left]\right[{\mathrm{n}}_2-{\mathrm{n}}_1+1\left]\right\}$$/2$
• Where, ${\mathrm{n}}_1=$$2$
• And, ${\mathrm{n}}_2=$$7$
• So, No. of spectral lines$=15$.

So, option[C] is incorrect.

[D]$10$

• No. of spectral lines$=\left\{\right[{\mathrm{n}}_2-{\mathrm{n}}_1\left]\right[{\mathrm{n}}_2-{\mathrm{n}}_1+1\left]\right\}$$/2$
• Where, ${\mathrm{n}}_1=$$2$
• And, ${\mathrm{n}}_2=$$7$
• So, No. of spectral lines$=15$.

So, option[D] is incorrect.

Hence, option[B]$15$ is the no. of spectral lines possible.