Ncert Exercises & Solutions

What is the minimum energy that must be given to a H-atom in ground state so that it can emit an $H_{γ}$ line in Balmer series? If the angular momentum of the system is conserved, what would be the angular momentum of such $H_{γ}$ photon?

Hint: The energy required will be equal to the energy difference between the transition levels.

H_{γ}

in Balmer series corresponds to transition n = 5 to n = 2. So, the electron in the ground state, i.e., from n = 1 must first be placed in state n = 5.

The energy required for the transition from n = 1 to n = 5 is given by

= E_{5} - E_{1} = - 0.54 + 13.6 = 13.06 eV

Step 2: Conserve the angular momentum.

Since, angular momentum is conserved,

angular momentum corresponding to

H_{γ}

photon = change in angular momentum of the electron

= L_{5} - L_{2} = 5 \frac{h}{2 π} - 2 \frac{h}{2 π} = 3 \frac{h}{2 π} = 3 \times 1.06 \times 10^{- 34}

= 3.18 \times 10^{- 34} kg - m^{2} / s

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