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Atoms and Nuclei question

2015 · Shift 0 · Q43
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Atoms and Nuclei question

2015 · Shift 0 · Q43

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1
As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :
  1. A
    kinetic energy decreases, potential energy increases but total energy remains same
  2. B
    kinetic energy and total energy decrease but potential energy increases
  3. C
    its kinetic energy increases but potential energy and total energy decrease
  4. D
    kinetic energy, potential energy and total energy decrease
View written solutionFree

Correct answer: C

  1. Energy of an electron in a hydrogen-like atom

For a hydrogen-like atom, the total energy in the nnnth orbit is

En=−13.6Z2n2 eVE_n=-\frac{13.6Z^2}{n^2}\,\text{eV}En​=−n213.6Z2​eV

So, when an electron goes from an excited state to the ground state, nnn decreases.

Hence,

  • EnE_nEn​ becomes more negative,
  • therefore total energy decreases.
  1. Relation between kinetic and potential energy

For an electron bound by Coulomb force:

U=−Ze24πε0rU = -\frac{Ze^2}{4\pi\varepsilon_0 r}U=−4πε0​rZe2​

so potential energy is negative.

Using the virial theorem for inverse-square force:

K=−12UquadandE=K+U=−K=U2K = -\frac{1}{2}U quad \text{and} \quad E = K+U = -K = \frac{U}{2}K=−21​UquadandE=K+U=−K=2U​

Thus:

  • If the electron goes to a lower orbit, radius rrr decreases.
  • Then UUU becomes more negative, so potential energy decreases.
  • Since K=−EK=-EK=−E, and EEE becomes more negative, kinetic energy increases.
  1. Check each option

  • A: kinetic energy decreases, potential energy increases, total energy same
    ⇒\Rightarrow⇒ False.

  • B: kinetic energy and total energy decrease, potential energy increases
    ⇒\Rightarrow⇒ False.

  • C: kinetic energy increases but potential energy and total energy decrease
    ⇒\Rightarrow⇒ True.

  • D: kinetic energy, potential energy and total energy decrease
    ⇒\Rightarrow⇒ False because kinetic energy actually increases.

  1. Final answer

The correct option is:

C\boxed{\text{C}}C​
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