In which of the following transition the wavelength be minimum ? a)n=5 to n=4 b)n=4 to n=3 c)n=3 to n=2 d)n=2 to n=1

Asked by akshadevdm2020 | 22nd May, 2021, 03:43: PM

Expert Answer:

Wavelength begin mathsize 14px style lambda subscript m n end subscript end style of spectral line that arises due to transition from orbital quantum number m to orbital quantum number n is given as
 
begin mathsize 14px style 1 over lambda subscript m n end subscript space equals space R space open parentheses 1 over m squared space minus space 1 over n squared close parentheses end style

where R is Rydberg constant .
 
Reciprocal of wavelength for all the transitions are tabulated below
 
Transition  Eqn. for (1/λ) 1/λ
n=5 to n=4
begin mathsize 14px style 1 over lambda subscript 54 space equals space R space open parentheses 1 over 4 squared space minus space 1 over 5 squared close parentheses end style
R × 0.0225
n = 4 to n = 3
begin mathsize 14px style 1 over lambda subscript 43 space equals space R space open parentheses 1 over 3 squared space minus space 1 over 4 squared close parentheses end style
 R × 0.0486
n = 3 to n = 2
begin mathsize 14px style 1 over lambda subscript 32 space equals space R space open parentheses 1 over 2 squared space minus space 1 over 3 squared close parentheses end style
 R × 0.1389
n = 2 to n = 1
begin mathsize 14px style 1 over lambda subscript 21 space equals space R space open parentheses 1 over 1 squared space minus space 1 over 2 squared close parentheses end style
 R × 0.5
 
From above table , it can be seen that for the transition from n=2 to n=1 , Reciprocal of wavelength is maximum.
 
Hence wavelength is minimum for transition from n=2  to n=1

Answered by Thiyagarajan K | 22nd May, 2021, 04:56: PM

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