Exams › JEE Main › Chemistry
Which of the following statements regarding the energy of the stationary state is true in the following one-electron system ? (1) −1.09 × 10^−18 J for second orbit of H atom. (2) +2.18 × 10^−18 J for second orbit of He^+ ion (3) +8.72 × 10^−18 J for first orbit of He^+ ion (4) −2.18 × 10^−18 J for third orbit of Li^2+ ion
- −1.09 × 10^−18 J for second orbit of H atom.
- +2.18 × 10^−18 J for second orbit of He^+ ion
- +8.72 × 10^−18 J for first orbit of He^+ ion
- −2.18 × 10^−18 J for third orbit of Li^2+ ion
Correct answer: −2.18 × 10^−18 J for third orbit of Li^2+ ion
Solution
The energy of an electron in a hydrogen-like atom is given by the formula E = -Z² * 13.6 eV / n², where Z is the atomic number and n is the principal quantum number. For Li²⁺, which has Z = 3, the energy for the third orbit (n=3) is calculated to be negative, indicating a bound state, and results in -2.18 × 10^−18 J, making this statement correct.
Related JEE Main Chemistry questions
- At what wavenumber does the first line of the hydrogen Balmer series occur in the atomic spectrum?
- In the hydrogen emission spectrum, a spectral series has its limit at 12186.3 cm$^{-1}$. This series is identified as
- Two rapidly moving particles X and Y have de Broglie wavelengths of 1 nm and 4 nm, respectively. If the mass of X is nine times the mass of Y, what is the ratio of their kinetic energies, X:Y?
- Given that Planck’s constant is $6.63 \times 10^{-34}$ J s and the speed of light is $3.0 \times 10^8$ m s$^{-1}$, which of the following is nearest to the wavelength, in nanometres, of light having frequency $8 \times 10^{15}$ s$^{-1}$?
- A lithium ion and a proton are each accelerated through the same potential difference. If their de Broglie wavelengths are $\lambda_1$ and $\lambda_2$, respectively, and $m_{\text{Li}} = 9m_p$, what is the ratio $\lambda_1 : \lambda_2$?
- If the uncertainties in position and momentum are the same, what is the uncertainty in velocity?
⚔️ Practice JEE Main Chemistry free + battle 1v1 →