SATHEE: Modern Physics 5 Question 32

Modern Physics 5 Question 32

35. The element curium $_{96}^{248} C m$ has a mean life of $10^{13} s$ . Its primary decay modes are spontaneous fission and $α$ -decay, the former with a probability of $8$ and the latter with a probability of $92$ , each fission releases $200 M e V$ of energy. The masses involved in decay are as follows :

$(1997, 5$ M)

$_{96}^{248} C m = 248.072220 u$ ,

$_{94}^{244} P u = 244.064100 u$ and $_{2}^{4} H e = 4.002603 u$ . Calculate the power output from a sample of $10^{20} C m$ atoms.

$(1 u = 931 M e V / c^{2})$

Show Answer

Solution:

The reaction involved in $α$ -decay is

$_{96}^{248} C m \to_{94}^{244} P u +_{2}^{4} H e$

Mass defect

$Δ m =$ mass of $_{96}^{248} C m - mass$ of $_{94}^{244} P u -$ mass of $_{2}^{4} H e$

$= (248.072220 - 244.064100 - 4.002603) u$

$= 0.005517 u$

Therefore, energy released in $α$ -decay will be

$E_{α} = (0.005517 \times 931) M e V = 5.136 M e V$

Similarly, $E_{fission} = 200 M e V$ (given)

Mean life is given as $t_{mean} = 10^{13} s = 1 / λ$

$∴$ Disintegration constant $λ = 10^{- 13} s^{- 1}$

Rate of decay at the moment when number of nuclei are $10^{20}$

$\begin{aligned} = λ N = (10^{- 13}) (10^{20}) \\ = 10^{7} disintegration per second \end{aligned}$

Of these disintegrations, $8$ are in fission and $92$ are in $α$ -decay.

Therefore, energy released per second

$\begin{aligned} = (0.08 \times 10^{7} \times 200 + 0.92 \times 10^{7} \times 5.136) M e V \\ = 2.074 \times 10^{8} M e V \end{aligned}$

$∴$ Power output (in watt)

$\begin{aligned} = energy released per second (J / s) \\ = (2.074 \times 10^{8}) (1.6 \times 10^{- 13}) \end{aligned}$

$∴$ Power output $= 3.32 \times 10^{- 5} W$

पिछला

अगला

Modern Physics 5 Question 32

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

Modern Physics 5 Question 32

35. The element curium 96248Cm has a mean life of 1013s. Its primary decay modes are spontaneous fission and α-decay, the former with a probability of 8 and the latter with a probability of 92, each fission releases 200MeV of energy. The masses involved in decay are as follows :

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

Menu