Question

# Assume an imaginary world where angular momentum is quantized to even multiple. The longest possible wave length emitted by hydrogen in the visible spectrum is

A
484nm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
300nm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
400nm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
350nm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 484nmThe angular momentum is quantized to even multiple of ¯h, hencemvr=2nℏmv=2nℏrmv2=m2v2m=(2nℏ)2mrThe Coulomb's force of attraction is equal to the centripetal force.Ze24πϵ0r2=mv2rZe24πϵ0r2=(2nℏ)2mrrr=(2nℏ)24πϵ0mZe2Now, the binding energy of electron isBE=−Ze28πϵ0rBE=−Ze28πϵ0((2nℏ)24πϵ0mZe2) BE=−Z2e4m32πϵ20n2h2BE=−3.4n2eVFor longest possible wavelength in visible spectrum n2=4 and n1=1hν=−3.4[1−14]hν=−3.4(34)ν=−3.4×0.75hTherefore, the longest possible wavelength emitted by hydrogen in the visible spectrum is(in nm)λ=cνλ=hc3.4×0.75λ=12362.55λ=484 nm

Suggest Corrections
0
Join BYJU'S Learning Program
Select...
Related Videos
Bohr's Model of Atom
CHEMISTRY
Watch in App
Explore more
Join BYJU'S Learning Program
Select...