Which transition in hydrogen atomic spectrum will have the same wavelength as the transition, n = 4 to n = 2 energy level of he+ spectrum?
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HEYA
I WILL DENOTE LAMBDA WITH L
for he+ ion wave no. = 1/L = RZ²(1/n1²-1/n2²)
plug these values in it
n1 = 2
n2 = 4
z = 2 (atomic no. of he)
so we get
1/L = R(4)(1/4-1/16)
after solving this you will get ------
L = 4R/3
now desired transition for H with same wavelength as that of he+
will be
1/L = R(1²)(1/n1²-1/n2²)
put the value of L
3R/4 = R ( 1/n1²-1/n2²)
so by hit and trial method this will satisfy when
n1 = 1 and n2 = 2 .
I WILL DENOTE LAMBDA WITH L
for he+ ion wave no. = 1/L = RZ²(1/n1²-1/n2²)
plug these values in it
n1 = 2
n2 = 4
z = 2 (atomic no. of he)
so we get
1/L = R(4)(1/4-1/16)
after solving this you will get ------
L = 4R/3
now desired transition for H with same wavelength as that of he+
will be
1/L = R(1²)(1/n1²-1/n2²)
put the value of L
3R/4 = R ( 1/n1²-1/n2²)
so by hit and trial method this will satisfy when
n1 = 1 and n2 = 2 .
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