Question

The number of spectral lines that are possible when electrons in 7th shell in different hydrogen atoms return to the 2nd shell is:
A.12
B. 15
C. 14
D. 10

Answer 1

Hint: There are 5 spectral lines in hydrogen atoms namely Lyman , balmer, paschen, bracket and pfund.
Transition from the first shell to any other shell is called Lyman series.
Transition from the second shell to any other shell is called Balmer series.
Transition from the third shell to any other shell is called Paschen series.
Transition from the fourth shell to any other shell is called Bracket series.
Transition from the fifth shell to any other shell is called Pfund series.

Complete step by step solution:
Bohr's atomic model is based on the quantum theory of radiation and the classical concept of physics.
Postulates of bohr's atomic model are
(a) The path of the electron is circular. The force of attraction between electron and nucleus is equal to the centrifugal force of the moving electron.
(b) Electron revolve around the orbital that follows the rule that the angular momentum is an integral multiple of
$mvr=\dfrac{nh}{2\pi }$ (m = mass of electron, v = velocity of electron, r = radius of orbit)
(c) Electron remains in the orbit where it is stationery and it does not lose energy.
(d) Each stationary orbit is with definite amount of energy (E) and E1< E2 < E3
(E2-E1) > (E3 - E2) > (E2- E1).
The Energy of Electron
Total energy (E) = K.E. + P.E.
Now the formula to calculate the total number of spectral lines is
$\dfrac{(n2-n1)\times (n2-n1-1)}{2}$, when the electron returns from n2 to n1.
In this case n2 is 7 and n1 is 2.
So total number of spectral lines are =$\dfrac{(7-2)\times (7-2-1)}{2}=\dfrac{5\times 4}{2}$=10

So the correct option is c.

Note: The following are to be noted:
i.The Lyman series is in ultraviolet region
ii. The balmer series is in visible region
iii. The paschen , bracket, Pfund series are in the infrared region.