Question 3 of 8intermediate🔧 ApplyNumerical2 marks

The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?

Correct Answer

Given: Total energy E = –13.6 eV (ground state)

From the textbook, the relations between kinetic energy (K), potential energy (U), and total energy (E) are: K = e²/8πε₀r and U = –e²/4πε₀r E = K + U = –e²/8πε₀r

Step 1: From the above relations, we can see that: K = –E and U = 2E

Step 2: Substituting the given value: Kinetic energy K = –(–13.6 eV) = 13.6 eV

Step 3: Calculating potential energy: Potential energy U = 2 × (–13.6 eV) = –27.2 eV

Verification: E = K + U = 13.6 + (–27.2) = –13.6 eV ✓

Exercise: EXERCISES | Q: 12.4 | (Page 16)
For More Understanding

Explanation

The textbook provides the fundamental relations: K = e²/8πε₀r (kinetic energy), U = –e²/4πε₀r (potential energy), and E = K + U = –e²/8πε₀r (total energy). From these, we derive that K = –E and U = 2E. This is a standard result in Bohr's model where kinetic energy is always positive and equals the magnitude of total energy, while potential energy is twice the total energy and negative.

Solution Steps

  1. Step 1: Identify relations from textbook: K = e²/8πε₀r, U = –e²/4πε₀r, E = –e²/8πε₀r

  2. Step 2: Derive that K = –E and U = 2E from the relations

  3. Step 3: Calculate K = –(–13.6) = 13.6 eV

  4. Step 4: Calculate U = 2 × (–13.6) = –27.2 eV

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