Atoms And Nuclei Question 272

Question: In the Bohr’s model of hydrogen-like atom the force between the nucleus and the electron is modified as F=e24πε0(1r2+βr3), where β is a constant. For this atom, the radius of the nth orbit in terms of the Bohr radius (a0=ε0h2mπe2) is:

Options:

A) rn=a0nβ

B) rn=a0n2+β

C) rn=a0n2β

D) rn=a0n+β

Show Answer

Answer:

Correct Answer: C

Solution:

  • As F=mv2r=e24πε0(1r2+βr3) and mvr=nh2πv=nh2πmr
    m(nh2πmr)2×1r=e24πε0(1r2+βr3) or, a0n2r3=1r2+βr3(a0=ε0h2mπe2Given)
    r=a0n2β


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