A radioactive nucleus undergoes a series of decay according to the scheme

\( A\xrightarrow{α} A_1\xrightarrow{β} A_2\xrightarrow{α}A_3\xrightarrow{γ}A_4\)

If the mass number and atomic nubmer of A are 180 and 72 respectively, then what are these number for A_{4}?

[A] 172 and 69

[B] 174 and 70

[C] 176 and 69

[D] 176 and 70

An archaeologist analyses the wood in a prehistoric structure and finds that C^{14} (Half-life = 5700 years) to C^{12} is only one-third of that found in the cells [A] 5700 yr

[B] 2850 yr

[C] 1 1,400 yr

[D] 22,800yr

Unit of radioactivity is Rutherford. Its value is

[A] 3.7×10^{10} disintegration/s

[B] 3.7×10^{6} disintegration/s

[C] 1.0×10^{10} disintegration/s

[D] 1.0×10^{6} disintegration/s

The counting rate observed from a radioactive source at t = 0 was 1600 count/s and at t=8 s it was 100 count/s. The counting rate observed, as count/s at t = 6 s, will be

[A] 400

[B] 300

[C] 200

[D] 150

In the given nuclear reaction A, B, C, D, E represents _{92}U^{238}\(\xrightarrow{α}\)_{B}Th^{A}\(\xrightarrow{β} \) _{D}Pa^{C}\(\xrightarrow{E}\)_{92}U^{234}

[A] A =234, B = 90, C = 234, D=91, E =β

[B] A = 234, B – 90, C = 238, D = 94, E =α

[C] A = 238, B = 93, C = 234, D = 91, E = β

[D] A = 234, B = 90, C = 234, D = 93, E =α

1 curie is equal to

[A] 3×10^{10} disintegration/s

[B] 3.7×10^{7} disintegration/s

[C] 5×10^{7} disintegration/s

[D] 3.7×10^{10} disintegration/s

The half-life of a sample of a radioactive substance is 1 h. If 8×10^{10} atoms are present at t=0, then the number of atoms decayed in the duration t=2h to t=4h will be

[A] 2×10^{10}

[B] 1.5×10^{10}

[C] zero

[D] infinity

Threshold frequency for a metal is 10^{15} Hz. Light of λ= 4000Å falls on its surface. Which of the following statements is correct?

[A] No photoelectric emission takes place

[B] Photoelectron come out with zero speed

[C] Photoelectron come out with 10^{3} m/s speed

[D] Photoelectron come out with 10^{5} m/s speed

Half-life of a radioactive substance is 20 min. Difference between points of time when it is 33% disintegrated and 67% disintegrated is approximately

[A] 10 min

[B] 20 min

[C] 30 min

[D] 40 min

A and B are two radioactive substances whose half-lives are 1 and 2 years respectively. Initially 10 g of A and 1 g of B is taken. The time (approximate) after which they will have same quantit [A] 6.62 yr

[B] 5 yr

[C] 3.2yr

[D] 7 yr

Half-life of a radioactive substance is 20 min. The time between 20% and 80% decay will be

[A] 20 min

[B] 40 min

[C] 30 min

[D] 25 min

After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is

[A] 6000

[B] 9000

[C] 3000

[D] 24000

If 10% of radioactive material decays in 5 days, then the amount of the original material left after 20 days is approximately

[A] 60%

[B] 65%

[C] 70%

[D] 75%

In a sample of radioactive material, what fraction of the initial number of active nuclei will remain undisintegrated after half of a half-life of the sample?

[A] \( \sqrt{2}-1\)

[B] \( \frac{1}{\sqrt{2}}\)

[C] \( \frac{1}{2\sqrt{2}}\)

[D] \( \frac{1}{4}\)

90% of a radioactive sample is left undecayed after time t has elapsed. What percentage of the initial sample will decay in a total time 21?

[A] 20%

[B] 19%

[C] 40%

[D] 38%

In a radioactive sample the fraction of initial number of radioactive nuclei, which remains undecayed after n mean lives is

[A] \( \frac{1}{e^n}\)

[B] e^{n}

[C] \( (1-\frac{1}{e^n})\)

[D] \( (\frac{1}{e-1})^n\)

A stationary radioactive nucleus of mass 210 units disintegrates into an alpha particle of mass 4 units and residual nucleus of mass 206 units. If the kinetic energy of the alpha particle is E, [A] \( \frac{2}{105} \)E

[B] \( \frac{2}{103} \)E

[C] \( \frac{103}{105} \)E

[D] \( \frac{103}{2} \)E

A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safel [A] 128h

[B] 24 h

[C] 6h

[D] 12 h

An atom of mass number A and atomic number Z emits successively a γ-ray, a β-particle, and α-particle. The mass number and the atomic number of the end product are

[A] A – 4, Z – 4

[B] A, Z + 1

[C] A – 4, Z + 2

[D] A – 4, Z – 1

The dacay constant of a radioactive substance is λ Its half-life and mean-life, respectively are

[A] \( \frac{1}{λ} \) and log_{e}2

[B] \( \frac{log_e2}{λ}\) and \( \frac{1}{λ}\)

[C] \( 2log_e2 and \frac{1}{λ} \)

[D] \( \frac{1}{λ}\) and \( \frac{1}{λ}\)

A β-particle is emitted by a radioactive nucleus at the time of conversion of a

[A] neutron into a proton

[B] proton into a neutron

[C] nucleon into energy

[D] positron into energy

Atomic mass number of an element is 232 and its atomic number is 90. The end product if this radioactive element is an isotope of lead (_{82}Pb^{208}). The number of alpha and b [A] α = 3 and β = 3

[B] α = 6 and β = 4

[C] α = 6 and β = 2

[D] α = 1 and β = 6

The decay constant of a radioactive element is defined as the reciprocal of the time interval after which the number of atoms of the radioactive element falls to nearly

[A] 50% of its original number

[B] 36.8% of its original number

[C] 63.2% of its original number

[D] 75% of its original number

# Modern Physics Mock Test-4

CategoriesNEET IIT Physics