JEE Main 2025 · 29 January · evening · Single correct · +4 / −1

For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n?
[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]

  1. (a)
    Option (a)
  2. (b)
    Option (b)
  3. (c)
    Option (c)
  4. (d)
    Option (d)
Answer and solution

Answer (d)

Solution

Chemistry ma’am · 4 steps

Read the Bohr energy formula twice: once for the sign of E, once for the power of Z.

  1. Bohr energy formula. For a hydrogen-like species with one electron, the energy of the nth stationary state is given below. With n fixed, 13.6/n² is just a constant.

    Eₙ = -13.6 Z²/n² eV

  2. Check the sign. The minus sign means a bound electron always has negative energy, so the curve must lie below the Z axis. That rules out (b) and (c).
  3. Check the shape. E varies as Z², not Z, so the plot is a parabola, not a straight line. As Z grows it falls more and more steeply, starting flat at the origin. That rules out the straight line in (a).
  4. So. The graph must be negative and curve downward like -Z². Only (d) shows this.

The idea to keep. For any graph question, write the formula first. The sign tells you which side of the axis the curve sits on, and the power tells you whether it is a line or a curve.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Atomic Structure

Asked about 170 times in JEE Main since 2020. This question is from 2025.