Question

When a sample of hydrogen atoms is irradiated by electromagnetic radiations of suitable wavelength,
all the electrons jump from the ground state to the fifth orbit. As the electrons can not remain
permanently in the fifth orbit, they de-excites to the ground state making one or more than one
transitions. Each transition results the emission of an electromagnetic radiation of a particular
wavelength. When these radiations pass through a prism, they deviate with different angles, resulting
the spectral lines.
What are the maximum and minimum number of spectral lines respectively .( if the sample is containing
only one atom)?
(A) 5,2
(B) 4,1
(C) 6,3
(D) 10,4
What is the maximum number of spectral lines, if the sample is containing only two atoms?
(A) 5
(B) 6
(C)
(D) 10
What should be the minimum number of hydrogen atoms in the sample to get a maximum of 10
spectral lines?
(A) B
(B) 5
(C) 7
(D) 10​

Answer 1

1. d

2. b

3. d

Explanation:

When an electron jumps from 0 shell rom 5th stationary state (n=5) to k shell i.e to 1st state n=1 the distinct spectral lines which can be obtained are:-

1. Four lyman series: from n = 2, 3, 4, 5 to n = 1
2. Three balmer series: from n = 3, 4, 5 to n = 2
3. Two paschen series: from n = 4, 5 to n = 3
4. One bracket series lines: from n = 5 to n = 4

Number of hydrogen atoms we require to observe these transitions:

1 - Atom: goes from 5 --> 4 --> 3 --> 2 -->1;

2 - Atom: goes from 5 --> 4 --> 2--> 1;

3 - Atom: goes from 5 --> 2 --> 1;

4 - Atom: goes from 5 --> 3 -->1;

5 - Atom: goes from 5 --> 4 -->1;

6 - Atom: goes from 5 --> 4 --> 3 --> 2 -->1;

7 - Atom: goes from 5 -->1;

Hence, all the above ten transitions can be covered from maximum six (6) number of hydrogen atoms.