SATHEE: Atoms And Nuclei Question 311

Atoms And Nuclei Question 311

Question: The ionization energy of a hydrogen like Bohr atom is 4 Rydbergs. Find the wavelength of the radiation emitted when the electron jumps from the first excited state to the ground state

Options:

A) $300 A^{\circ}$

B) $2.5 \times 10^{- 11} m$

C) $100 A^{\circ}$

D) $1.5 \times 10^{- 11} m$

Show Answer

Answer:

Correct Answer: A

Solution:

$E_{n} = - \frac{I . E .}{n^{2}}$ for Bohr “s hydrogen atom. Here, $I . E / = 4 R ∴ E_{n} = \frac{- 4 R}{n^{2}}$

$∴ E_{2} - E_{1} = \frac{- 4 R}{2^{2}} - (- \frac{4 R}{l^{2}}) = 3 R$ ..(i) $E_{2} - E_{1} = h v = \frac{h c}{λ}$ .(ii) From (i) and (ii)

$∴ λ = \frac{h c}{3 R} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{2.2 \times 10^{- 18} \times 3} = 300 \overset{o}{A},$

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Atoms And Nuclei Question 311

Question: The ionization energy of a hydrogen like Bohr atom is 4 Rydbergs. Find the wavelength of the radiation emitted when the electron jumps from the first excited state to the ground state

Options:

Answer:

Solution:

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