A beam of electrons is incident on hydrogen atoms initially in their ground states. Neglect atomic recoil. If the minimum electron kinetic energy needed to excite a hydrogen atom to the fourth Bohr orbit is (N ÷ 100) eV, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A beam of electrons is incident on hydrogen atoms initially in their ground states. Neglect atomic recoil. If the minimum electron kinetic energy needed to excite a hydrogen atom to the fourth Bohr orbit is (N ÷ 100) eV, find N.

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

For hydrogen, Eₙ = −13.6 ÷ n² eV. The excitation energy to the fourth orbit is ΔE = 13.6[1−1 ÷ 4²] = 13.6×15 ÷ 16 = 12.75 eV. Therefore, 12.75 eV = 1275 ÷ 100 eV. Hence N = 1275.