Answer:
(a) Yes, the atom is ionized; (b) 5.4 × 10⁻²⁰ J
Explanation:
(a) Will the atom ionize?
(i) Energy of atom
The formula for the energy levels of a hydrogen atom is:
[tex]E_{n}= -\dfrac{E_{0}}{n^{2}}[/tex]
where E₀ = 2.178 × 10⁻¹⁸ J
For n = 2.
[tex]E _{2}= -\dfrac{2.178 \times 10^{-18} \text{ J}}{2^{2}} = 5.445 \times 10^{-19} \text{ J}[/tex]
Thus, the energy needed to ionize the atom is 5.445× 10⁻¹⁹ J.
(ii) Energy of photon
E = \dfrac{\text{hc}}{\lambda} = \dfrac{6.626 \times 10^{-34} \text{ J$\cdot$ s}\times 2.998 \times 10^{8} \text{ m/s}}{332 \times 10^{-9}\text{ J}}= 5.98 \times 10^{-18} \text{ J}
This is more than the energy needed to ionize the atom.
Yes, the atom will be ionized.
(B) Kinetic energy of electrons
The kinetic energy of the electron is the difference between the energy of the photon and that needed to ionize the atom:
KE = E - IE = 5.98× 10⁻¹⁹ J - 5.445 × 10⁻¹⁹ J = 5.4 × 10⁻²⁰ J
