Question

Which of the following levels of H and He+ have same
energy respectively ?
(A) 1,2 (B) 3,4 (C) 2,4 (D) 3,6
(a) A and D
(b) A and B
(c) C and D
(d) A, C and D​

Answer 1

a and d

1,2and3,6 is level of and He

Answer 2

1,2 ; 2,4; 3,6 levels of H and He+ have the same energy respectively. The correct option is (d)A, C and D​.

Explanation:

The energy of a level of the Hydrogen atom is given by:

     $E_{n}^H =-2.18$ × $10^1^8 (\frac{Z^{2} }{n_{h} ^2} ) J$

   Since, for hydrogen, Z =1  

     $E_{n}^H$ =$-2.18$ × $10^1^8 (\frac{1}{n_{h} ^2} )$ J

The  energy of a level of the Helium  atom is given by:

$E_{n} ^H^e^+$ =  $-2.18$ × $10^1^8 (\frac{2^{2} }{n_{He} ^2} )$ J

If $n_{H}$=1 Then $n_{He}$=2

If $n_{H}$=2 Then $n_{He}$=4

If  $n_{H}$=3 Then $n_{He}$=6

Therefore,A, C, and D have the same energy