An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λ n ,   λ g be the de Broglie wavelength of the electron in the n t h state and the ground state respectively. Let ∧ n be the wavelength of the emitted photon in the…

Question

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let &#955; n , &#160; &#955; g be the de Broglie wavelength of the electron in the n t h state and the ground state respectively. Let &#8743; n be the wavelength of the emitted photon in the transition from the n t h state to the ground state. For large n, (A, B are constants)

Aicharya · Accepted Answer

2 &#960; r = n &#8907; n &#8907; n = 2 &#960; r n &#8756; r = r o n 2 &#8907; n = 2 &#960; n &#160; r o n 2 = n 2 &#960; r o &#160; &#160; &#8230; . . i 1 &#8743;&#8203; n = R 1 1 2 - 1 n 2 &#8743;&#8203; n = 1 R 1 + 1 n 2 - 1 &#8743;&#8203; n = 1 R 1 + 1 n 2 &#160; &#160; &#8230; &#8230; &#8230; . . ii from ( i ) and ( ii ) &#8743;&#8203; n = 1 R 1 + 4 n 2 r o 2 &#8907; n 2 = A + B &#8907; n 2

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let…

Solution