Question

Calculate the energy for the transition of an electron from the n=1 level to the n= 7 level of a hydrogen atom. AE = Joules Is this an Absorption (A) or an Emission (E) process?

Answer 1

From Bohr's model we have equation, E = - 2.178 $\times$ 10 ^-18 J ( Z ² / n ² )

Where, Z is nuclear charge and n is integer.

For Hydrogen atom, Z= 1.

Energy corresponding to state 1 is calculated as

E ₁ = - 2.178 $\times$ 10 ^-18 J ( Z ² / n ² ) = - 2.178 $\times$10 ^-18 J ( 1 ² / 1 ² ) = - 2.178$\times$ 10 ^-18 J

Energy corresponding to state 7 is calculated as

E ₇ = - 2.178 $\times$ 10 ^-18 J ( Z ² / n ² ) = - 2.178 $\times$ 10 ^-18 J ( 1 ² / 7 ² ) = - 4.445 $\times$ 10 ^-20 J

The change in energy when electrons jumps from n=1 to n=7 is

E = energy of final state (E ₇ ) - energy of initial state (E ₁)

E =( - 4.445 $\times$ 10 ^-20 J ) - ( - 2.178 $\times$ 10 ^-18 J ) = + 2.134 $\times$ 10 ^-18 J

+ sign indicates energy is absorbed during electronic transition.

ANSWER : E = + 2.134 $\times$ 10 ^-18 J

Process : Absorption

PART 2

Energy corresponding to state 1 is calculated as

E ₁ = - 2.178 $\times$ 10 ^-18 J ( Z ² / n ² ) = - 2.178 $\times$ 10 ^-18 J ( 1 ² / 1 ² ) = - 2.178 $\times$ 10 ^-18 J

Energy corresponding to state 5 is calculated as

E ₅ = - 2.178 $\times$ 10 ^-18 J ( Z ² / n ² ) = - 2.178 $\times$ 10 ^-18 J ( 1 ² / 5 ² ) = - 8.712 $\times$ 10 ^-20 J

The change in energy when electrons jumps from n=1 to n=5 is

E = energy of final state (E ₅ ) - energy of initial state (E ₁)

E =( - 8.712 $\times$ 10 ^-20 J ) - ( - 2.178 $\times$10 ^-18 J ) = + 2.091 $\times$ 10 ^-18 J

+ sign indicates energy is absorbed during electronic transition.

ANSWER : E = + 2.091 $\times$ 10 ^-18 J

Process : Absorption

PART 3

Energy corresponding to state 3 is calculated as

E ₃ = - 2.178 $\times$10 ^-18 J ( Z ² / n ² ) = - 2.178 $\times$ 10 ^-18 J ( 1 ² / 3 ² ) = - 2.420 $\times$ 10 ^-19 J

ANSWER : Energy = - 2.420 $\times$ 10 ^-19 J