SATHEE: Modern Physics 2 Question 36

Modern Physics 2 Question 36

35. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is $0.73 e V$ . The work function for sodium is $1.82 e V$ .

(1992, 10M) Find

(a) the energy of the photons causing the photoelectrons emission.

(b) the quantum numbers of the two levels involved in the emission of these photons.

(d) the recoil speed of the emitting atom assuming it to be at rest before the transition. (Ionization potential of hydrogen is $13.6 e V$ .)

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Answer:

Correct Answer: 35. $1.1 \times 10^{12}$

Solution:

(a) From Einstein’s equation of photoelectric effect, Energy of photons causing the photoelectric emission $=$ Maximum kinetic energy of emitted photons

+work function

or $E = K_{max} + W = (0.73 + 1.82) e V$

or $E = 2.55 e V$

(b) In case of a hydrogen atom,

$\begin{aligned} E_{1} = - 13.6 e V, E_{2} & = - 3.4 e V, E_{3} = - 1.5 e V \\ E_{4} & = - 0.85 e V \end{aligned}$

Since, $E_{4} - E_{2} = 2.55 e V$

Therefore, quantum numbers of the two levels involved in the emission of these photons are 4 and $2 (4 \to 2)$ .

$Δ L = L_{2} - L_{4} = 2 \frac{h}{2 π} - 4 \frac{h}{2 π} or Δ L = - \frac{h}{π}$

(d) From conservation of linear momentum

| Momentum of hydrogen atom $| = |$ Momentum of

or $m v = \frac{E}{c} (m =$ mass of hydrogen atom $)$

$v = \frac{E}{m c} = \frac{(2.55 \times 1.6 \times 10^{- 19} J)}{(1.67 \times 10^{- 27} k g) (3.0 \times 10^{8} m / s)}$

$v = 0.814 m / s$

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Modern Physics 2 Question 36

35. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is $0.73 e V$ . The work function for sodium is $1.82 e V$ .

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Modern Physics 2 Question 36

35. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is 0.73eV. The work function for sodium is 1.82eV.

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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35. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is $0.73 e V$ . The work function for sodium is $1.82 e V$ .