Exams › JEE Main › Physics

Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect ? (The Bohr radius is represented by a0). (1) The magnitude of the potential energy is double that of its kinetic energy on an average. (2) The probability density of finding the electron is maximum at the nucleus. (3) The total energy of the electron is maximum when it is at a distance a0 from the nucleus. (4) The electron can be found at a distance 2a0 from the nucleus.

1. The magnitude of the potential energy is double that of its kinetic energy on an average.
2. The probability density of finding the electron is maximum at the nucleus.
3. The total energy of the electron is maximum when it is at a distance a0 from the nucleus.
4. The electron can be found at a distance 2a0 from the nucleus.

Correct answer: The total energy of the electron is maximum when it is at a distance a0 from the nucleus.

Solution

For the 1s electron, virial theorem (|PE|=2*KE), max probability density at the nucleus, and finite probability at 2a0 are all correct. The incorrect statement is that total energy is maximum at distance a0 -- the total (orbital) energy is constant and independent of position, so option (3) is the wrong statement.

Related JEE Main Physics questions

• An electron in one Bohr orbit with principal quantum number n = n1 can produce 3 distinct spectral lines on de-excitation. In another orbit with principal quantum number n = n2, it can produce 6 distinct spectral lines. What is the ratio of the orbital speeds of the electron in these two orbits?
• An electron in a hydrogen atom is found in an excited state with energy equal to -3.4 eV. What is its angular momentum?
• A beam of electrons having energy 12.5 eV is directed at hydrogen gas in the gaseous state at room temperature. The emitted spectrum will contain:
• A hydrogen atom and a Li++ ion are each in their second excited state. If their electronic angular momenta are denoted by L_H and L_Li, and their energies by E_H and E_Li respectively, which statement is correct?
• For a proton–electron system, the interaction potential is V = V0 ln(r/r0), where r0 is a constant. If Bohr’s model is assumed to hold, how does the radius rₙ depend on the principal quantum number n?
• In the hydrogen spectrum, the longest wavelength in the ultraviolet region is 122 nm. The shortest wavelength in the infrared region, rounded to the nearest whole number, is

⚔️ Practice JEE Main Physics free + battle 1v1 →