Physics Nuclei
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An electron (of mass ) and a photon have the same energy in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is ( speed of light in vacuum)
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An electron (of mass ) and a photon have the same energy in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is ( speed of light in vacuum)
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The half-life of Au¹⁹⁸ is 2.7 days. The activity of 1.50 mg of Au¹⁹⁸ if its atomic weight is 198 g mol⁻¹ is, (Nₐ = 6×10²³ / mol)
The half-life of Au¹⁹⁸ is 2.7 days. The activity of 1.50 mg of Au¹⁹⁸ if its atomic weight is 198 g mol⁻¹ is, (Nₐ = 6×10²³ / mol)
A = Activity = λN = (ln (2)/t? /? ) N
N = (1.5×10? ³ / 198) × 6×10²³
A = (0.693 / (2.7×24×3600) × (1.5×10? ³ / 198) × 6×10²³ disintegration/s
A ≈ 1.32 × 10¹³ Bq = (1.32×10¹³ / 3.7×10¹? ) Ci ≈ 357 Ci
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Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.
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Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.
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N? /N? = e?
For 33% decay, N? /N? = 0.67 ≈ 2/3.
2/3 = e? ⇒ t? = (1/λ)ln (3/2)
For 67% decay, N? /N? = 0.33 ≈ 1/3.
1/3 = e? ⇒ t? = (1/λ)ln (3)
Δt = t? - t? = (1/λ) [ln (3) - ln (3/2)] = (1/λ)ln (2) = T? /? = 20 min
Upvote The nuclear activity of a radioactive element becomes (1/8)ᵗʰ of its initial value in 30 years. The half –life of radioactive element is __________ years.
The nuclear activity of a radioactive element becomes (1/8)ᵗʰ of its initial value in 30 years. The half –life of radioactive element is __________ years.
A = A? (1/2)?
A/A? = 1/8 = (1/2)³ ⇒ n = 3
t = n T½
30 = 3 T½
T½ = 10 years
Upvote The half-life of ¹?Au is 3 days. If atomic weight of ¹?Au is 198 g/mol then the activity of 2 mg of ¹?Au is [ in disintegration / second ] :
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The half-life of ¹?Au is 3 days. If atomic weight of ¹?Au is 198 g/mol then the activity of 2 mg of ¹?Au is [ in disintegration / second ] :
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t? /? = 3 days = 72 hours
dN/dt = λN = (ln2/t? /? ) N
= (0.693 × 6.02×10²³ × 2×10? ³) / (72 × 3600 × 198)
= 1.618 × 10¹³
= 16.18 × 10¹² disintegration/second
Upvote From the given data, the amount of energy required to break the nucleus of aluminium ²⁷₁₃Al is x × 10⁻³ J.
Mass of neutron = 1.00866 u
Mass of proton = 1.00726 u
Mass of Aluminium nucleus = 27.18846 u
(Assume 1 u corresponds to x J of energy)
(Round off to the nearest integer)
From the given data, the amount of energy required to break the nucleus of aluminium ²⁷₁₃Al is x × 10⁻³ J.
Mass of neutron = 1.00866 u
Mass of proton = 1.00726 u
Mass of Aluminium nucleus = 27.18846 u
(Assume 1 u corresponds to x J of energy)
(Round off to the nearest integer)
Binding Energy = (Δm)c²
= [Zmp + (A-Z)mn - MAl]c²
= [ (13×1.00726 + 14×1.00866) - 27.18846] u
= [ (13.09438 + 14.12124) - 27.18846] u
= [27.21562 - 27.18846] u
= 0.02716 u
= 0.02716 x = 27.16x × 10? ³
Upvote Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as : (where λ is the decay constant)
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Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as : (where λ is the decay constant)
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3N? /4 = N? e?
⇒ e? = 4/3
t? = (1/λ) ln (4/3)
t? = ln2/λ
t? - t? = (1/λ)ln2 - (1/λ)ln (4/3)
= (1/λ)ln (2/ (4/3) = (1/λ)ln (3/2)
Upvote Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half life of X is half of the life of Y. After three half lives of Y, number of nuclei of both are equal.
The ratio <!-- [if gte mso 9]><xml>
Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half life of X is half of the life of Y. After three half lives of Y, number of nuclei of both are equal.
The ratio <!-- [if gte mso 9]><xml>
Number of half lives of Y = 3
Number of half lives of X = 6 [As half life of X is half of that of Y].
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