A stationary hydrogen atom emits photon corresponding solution
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As for the transistion we know,
1
λ
= R(
1
n
2
f
−
1
n
2
i
)
where R = 1.097 ×
10
7
m ,
n
i
= 2 and
n
f
=1
so
1
λ
= 1.097 ×
10
7
(
1
1
−
1
4
)
so ,
1
λ
=
1.097 ×
10
7
× 3
4
= 0.82275 ×
10
7
so λ = 1.215 ×
10
−7
= =121.5 nm
so p = h/λ
so P(momentum) =
6.63×
10
−34
121.5 ×
10
−9
= 5.46 ×
10
−27
kg m/s
so by conservation of momentum:
v = p/m
or v =
5.46 ×
10
−27
1.67 ×
10
−27
= 3.269 m/s
this is the recoil speed of the atom
1
λ
= R(
1
n
2
f
−
1
n
2
i
)
where R = 1.097 ×
10
7
m ,
n
i
= 2 and
n
f
=1
so
1
λ
= 1.097 ×
10
7
(
1
1
−
1
4
)
so ,
1
λ
=
1.097 ×
10
7
× 3
4
= 0.82275 ×
10
7
so λ = 1.215 ×
10
−7
= =121.5 nm
so p = h/λ
so P(momentum) =
6.63×
10
−34
121.5 ×
10
−9
= 5.46 ×
10
−27
kg m/s
so by conservation of momentum:
v = p/m
or v =
5.46 ×
10
−27
1.67 ×
10
−27
= 3.269 m/s
this is the recoil speed of the atom
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