A light of energy 12.75 e V is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited

Question

A light of energy 12.75 e V is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is π x ​ × 1 0 − 17 e V s . The value of x is ______ (use h = 4.14 × 1 0 –15 e V s , c = 3 × 1 0 8 m s –1 )

TestHub · Accepted Answer

Let the electron jumped to n t h excited state. In the ground state, energy E = − 13.6 e V So, using relation 12.75 = 13.6 [ 1 2 1 ​ − n 2 1 ​ ] ⇒ 0.9375 = [ 1 − n 2 1 ​ ] ⇒ n 2 = 16 ⇒ n = 16 ​ = 4 Now, angular momentum, L = 2 π nh ​ = 2 π 4 h ​ = π 2 h ​ = π 2 ​ × 4.14 × 1 0 − 15 = π 828 × 1 0 − 17 ​ e V s Hence, the value of x = 828 .

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