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Question:

Hydrogen (1H1), Deuterium (1H2), singly ionised Helium (2He4)+ and doubly ionised lithium (3Li6)++ all have one electron around the nucleus. Consider an electron transition from n=2 to n=1. If the wavelengths of emitted radiation are λ1, λ2, λ3 and λ4 respectively then approximately which one of the following is correct?

λ1=2λ2=3λ3=4λ4

4λ1=2λ2=2λ3=λ4

λ1=λ2=4λ3=9λ4

λ1=2λ2=2λ3=λ4

Solution:

Answer is C
We know that, 1/λ = Rz²(1/1² - 1/2²)
where z= atomic number
z = 1 for hydrogen and deuterium
z = 2 for singly ionised Helium
z = 3 for doubly ionised lithium
Solving above, we get λ1 = λ2 = 4λ3 = 9λ4