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प्रश्न
Define the terms (i) half-life (T1/2) and (ii) average life (τ). Find out their relationships with the decay constant (λ).
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उत्तर
Half-life
The half-life of a radioactive substance is defined as the average time for which the nuclei of the atoms of the radioactive substance exist.
`t = t_(1/2)`
`R =1/2R_0`
`∴ t_(1/2)=(1n2)/λ`
`=(0.693)/4`
Average life or mean-life (τ):
`tau``=(λN_0int_0^oo te^(-λ1)dt)/N_0`
= `λint_0^oo te^(-λ1)dt`
`tau=1/lambda`
`∴ T_(1/2)=(1n2)/λ = tau 1n2`
संबंधित प्रश्न
Write symbolically the nuclear β+ decay process of `""_6^11C` Is the decayed product X an isotope or isobar of (`""_6^11C`)? Given the mass values m (`""_6^11C`) = 11.011434 u and m (X) = 11.009305 u. Estimate the Q-value in this process.
Obtain the binding energy (in MeV) of a nitrogen nucleus `(""_7^14"N")`, given `"m"(""_7^14"N")` = 14.00307 u.
What is meant by the terms half-life of a radioactive substance and binding energy of a nucleus?
Define half-life of a radioactive substance
What characteristic property of nuclear force explains the constancy of binding energy per nucleon (BE/A) in the range of mass number ‘A’ lying 30 < A < 170?
In which of the following decays the atomic number decreases?
(a) α-decay
(b) β+-decay
(c) β−-decay
(d) γ-decay
Answer the following question.
Draw the curve showing the variation of binding energy per nucleon with the mass number of nuclei. Using it explains the fusion of nuclei lying on the ascending part and fission of nuclei lying on the descending part of this curve.
Tritium is an isotope of hydrogen whose nucleus Triton contains 2 neutrons and 1 proton. Free neutrons decay into `p + bare + barν`. If one of the neutrons in Triton decays, it would transform into He3 nucleus. This does not happen. This is because ______.
Nuclei with magic no. of proton Z = 2, 8, 20, 28, 50, 52 and magic no. of neutrons N = 2, 8, 20, 28, 50, 82 and 126 are found to be very stable.
(i) Verify this by calculating the proton separation energy Sp for 120Sn (Z = 50) and 121Sb = (Z = 51).
The proton separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by `S_P = (M_(z-1^' N) + M_H - M_(ZN))c^2`.
Given 119In = 118.9058u, 120Sn = 119.902199u, 121Sb = 120.903824u, 1H = 1.0078252u.
(ii) What does the existance of magic number indicate?
Calculate the values of x and y in the following nuclear reaction.
\[\ce{^227_89Ac -> ^211_82Pb + x[^4_2He]+ y[^0_-1e]}\]
