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Physics Nuclei Nuclei

The activity of a radioactive sample falls from $700 s^{- 1}$ to $500 s^{- 1}$ in 30 minutes. Its half life is close to

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alok kumar singh

Contributor-Level 10

$A = A_{0} e^{- λ t}$

$\begin{array}{r} 500 = 700 e^{- λ t} \\ λ t = l n ? \frac{7}{5} \\ \frac{l n ? 2}{t_{1 / 2}} * 30 = l n ? \frac{7}{5} \\ ? t_{1 / 2} = \frac{l n ? 2 * 30}{l n ? \frac{7}{5}} \end{array}$

$t_{1 / 2} = 61.8 m i n \approx 62 m i n$

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Physics Nuclei Class 12th

What is the half – life period of a radioactive material if its activity drops to 1/16^th of its initial value in 30 years?

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alok kumar singh

Contributor-Level 10

$A = \frac{A_{0}}{16} = \frac{A_{0}}{2^{30 / t_{1 / 2}}} \Rightarrow 2^{4} = 2^{30 / t_{1 / 2}}$

$\Rightarrow \frac{A_{0}}{16} = \frac{A_{0}}{2^{30 / t_{1 / 2}}} \Rightarrow 2^{4} = 2^{30 / t_{1 / 2}}$

$\Rightarrow t_{1 / 2} = \frac{30}{4} = 7.5$ years

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Physics Nuclei Class 12th

Read the following statements:

(A) Volume of the nucleus is directly proportional to the mass number.

(B) Volume of the nucleus is independent of mass number.

(C) Density of the nucleus is directly proportional to the mass number.

(D) Density of nucleus is directly proportional to the cube root of the mass number.

(E) Density of the nucleus is independent of the mass number.

Choose the correct option from the following options

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alok kumar singh

Contributor-Level 10

Radius, R = R₀A^1/3

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Physics Nuclei Class 12th

The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8} t h$ of its original mass to disintegrate will be:

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Vishal Baghel

Contributor-Level 10

$t_{\frac{1}{2}} = 60 d a y s$

at t = 0 $\frac{m}{m_{0}} \to$ 0

$a t t \to \frac{m}{m_{0}} (1 - \frac{7}{8})$

= $\frac{m}{8 m_{0}} \to \frac{7}{8} (\frac{m}{m_{0}})$

$\Rightarrow \frac{1}{2^{3}} = \frac{1}{2^{(\frac{t}{60})}} \Rightarrow \frac{t}{60} = 3$

t = 180 days

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Physics Nuclei Nuclei

Two radioactive materials A and B have decay constants 25 $λ$ and 16 $λ$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be “e” after a time $\frac{1}{a λ} .$ The value of a is__________.

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alok kumar singh

Contributor-Level 10

$λ_{A} = 25 λ,$ $λ_{B} = 16 λ$

At t = 0 Þ N_A = N_B = N₀

after t = $\frac{1}{a λ} : - \frac{N_{B}}{N_{A}} = \frac{N_{0} e^{- 16 λ t}}{N_{0} e^{- 25 λ t}} = e^{(25 λ - 16 λ) t}$

->e = $e^{(9 λ \frac{1}{a λ})}$

$\Rightarrow \frac{9}{a} = 1 \Rightarrow a = 9$

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Physics Nuclei Class 12th

Two radioactive materials A and B have decay constants 25 $λ$ and 16 $λ$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be “e” after a time $\frac{1}{a λ} .$ The value of a is__________.

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Payal Gupta

Contributor-Level 10

$λ_{A} = 25 λ,$ $λ_{B} = 16 λ$

At t = 0 N_A = N_B = N₀

after t = $\frac{1}{a λ} : - \frac{N_{B}}{N_{A}} = \frac{N_{0} e^{- 16 λ t}}{N_{0} e^{- 25 λ t}} = e^{(25 λ - 16 λ) t}$

e = $e^{(9 λ \frac{1}{a λ})}$

$\Rightarrow \frac{9}{a} = 1 \Rightarrow a = 9$

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Physics Nuclei Class 12th

A sample contains 10^-2kg each of two substances A and B with half lives 4s and 8s respectively. The ration of their atomic weights is 1 : 2. The ratio of the amounts of A and B after16s is $\frac{x}{100}$ . The value of x is ______.

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Payal Gupta

Contributor-Level 10

$f o r A, t_{\frac{1}{2}} = 4 s e c$

$= m A_{0} e^{-} \frac{0.693}{4} * 16$

$m_{A} = m_{A 0} e^{- 4 * 0.693}$ - (1)

for B,

for B, $t_{\frac{1}{2}} = 8 s e c$

$m_{B} = m_{B_{0}} e^{- 2 * 0.693}$ - (2)

$\frac{m_{A}}{m_{B}} = \frac{m_{A O}}{m_{B O}} \frac{e^{- 4} * 0.693}{e^{- 2} * 0.693}$

$\frac{m_{A}}{m_{B}} = \frac{25}{100} = \frac{x}{100} x = 25$

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Physics Nuclei Class 12th

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in (B) and 'C' 6.4 MeV per nucleon. The energy Q released per fission will be :

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Vishal Baghel

Contributor-Level 10

$A \to^{105} B +^{115} C$

$\Rightarrow Q = [105 * 6.4 + 115 * 6.4] - [220 * 5.6] M e v$

Q = 176 MeV

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Physics Nuclei Class 12th

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6/25% of its initial value. The value of x is___________.

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Payal Gupta

Contributor-Level 10

According to Nuclear activity, we can write

$N_{0} \overset{t_{\frac{1}{2}}}{\to} \frac{N_{0}}{2} \overset{t_{\frac{1}{2}}}{\to} \frac{N_{0}}{4} \overset{t_{\frac{1}{2}}}{\to} \frac{N_{0}}{8} \overset{t_{\frac{1}{2}}}{\to} \frac{N_{0}}{16} = (0.0625) N_{0}$

Time required = 4 * $t_{\frac{1}{2}} = 20 y r s$

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2 months ago

Physics Nuclei Nuclei

A liquid of density 750 kgm^-3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A₁ = 1.2 * 10^-2m² to A₂ = $\frac{A_{1}}{2} .$ The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is_________ * 10^-3m³s^-1.

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alok kumar singh

Contributor-Level 10

Given A₂ = $\frac{_{}}{}$ $\frac{A_{1}}{2}$

Bernoulli's b/w (1) & (2)

$\frac{P_{1}}{ρ g} + \frac{v_{1}^{2}}{2 g} + z_{1} = \frac{ρ_{2}}{ρ g} + \frac{v_{2}^{2}}{2 g} + z_{2}$

[z₁= z₂]

$\frac{P_{1} - P_{2}}{ρ g} = \frac{v_{2}^{2} - v_{1}^{2}}{2 g}$

[Q = A₁V₁ = A₂V₂]

$\frac{4500}{750} = \frac{{(\frac{Q}{A_{2}})}^{2}}{2} - {(\frac{Q}{A_{1}})}^{2}$

$12 = Q^{2} [\frac{1}{A_{2}^{2}} - \frac{1}{A_{1}^{2}}]$

$Q = 2 A_{1} = 2 * 1.2 * 1 0^{- 2}$

= 2.4 * 10^-2 m³ /sec

= 24 * 10^-3 m³ /sec

= 24

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