SATHEE: Modern Physics 5 Question 34

Modern Physics 5 Question 34

37. Characteristic $X$ -rays of frequency $4.2 \times 10^{18} H z$ are produced when transitions from $L$ -shell to $K$ -shell take place in a certain target material. Use Mosley’s law to determine the atomic number of the target material. Given Rydberg’s constant $R = 1.1 \times 10^{7} m^{- 1}$ .

(2003, 2M)

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Solution:

Mass defect in the given nuclear reaction :

$\begin{aligned} Δ m & = 2 (mass of deuterium) - (mass of helium) \\ = 2 (2.0141) - (4.0026) = 0.0256 \end{aligned}$

Therefore, energy released

$\begin{aligned} Δ E & = (Δ m) (931.48) M e V = 23.85 M e V \\ = 23.85 \times 1.6 \times 10^{- 13} J = 3.82 \times 10^{- 12} J \end{aligned}$

Efficiency is only $25$ , therefore,

$\begin{aligned} 25 & = 9.55 \times 10^{- 13} J \end{aligned}$

i.e, by the fusion of two deuterium nuclei, $9.55 \times 10^{- 13} J$ energy is available to the nuclear reactor.

Total energy required in one day to run the reactor with a given power of $200 M W$ :

$E_{Total} = 200 \times 10^{6} \times 24 \times 3600 = 1.728 \times 10^{13} J$

$∴$ Total number of deuterium nuclei required for this purpose

$\begin{aligned} n & = \frac{E_{Total}}{Δ E / 2} = \frac{2 \times 1.728 \times 10^{13}}{9.55 \times 10^{- 13}} \\ = 0.362 \times 10^{26} \end{aligned}$

$∴$ Mass of deuterium required

$= ($ Number of $g$ -moles of deuterium required $) \times 2 g$

$= \frac{0.362 \times 10^{26}}{6.02 \times 10^{23}} \times 2 = 120.26 g$

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Modern Physics 5 Question 34

Solution:

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Modern Physics 5 Question 34

37. Characteristic X-rays of frequency 4.2×1018Hz are produced when transitions from L-shell to K-shell take place in a certain target material. Use Mosley’s law to determine the atomic number of the target material. Given Rydberg’s constant R=1.1×107m−1.

Solution:

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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