Radioactivity
PHXII13:NUCLEI

364034 Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_{A}\) and \(\lambda_{B}\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.

1 \(\lambda_{A}=2 \lambda_{B}\)
2 \(\lambda_{A}=\lambda_{B}\)
3 \(\lambda_{A}=\lambda_{B} \ln 2\)
4 \(\lambda_{A} \ln 2=\lambda_{B}\)
PHXII13:NUCLEI

364035 During mean life of a radioactive element, the fraction that disintegrates is

1 \(\frac{1}{e}\)
2 \(\frac{{e - 1}}{e}\)
3 \(e\)
4 \(\frac{e}{{e - 1}}\)
PHXII13:NUCLEI

364036 If a radioactive element having half-life of \(30\;\min \) is undergoing beta decay, the dfraction of radioactive element remains undecayed after \(90\;\min \) will be

1 \(\dfrac{1}{8}\)
2 \(\dfrac{1}{16}\)
3 \(\dfrac{1}{4}\)
4 \(\dfrac{1}{2}\)
PHXII13:NUCLEI

364037 Decay constants of two radio - active samples \(A\) and \(B\) are 15\(x\) and 3\(x\) respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in \(A\) and \(B\) after a time 1/6\(x\) is

1 \(e\)
2 \({e^2}\)
3 \({e^{ - 1}}\)
4 \({e^{ - 2}}\)
PHXII13:NUCLEI

364034 Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_{A}\) and \(\lambda_{B}\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.

1 \(\lambda_{A}=2 \lambda_{B}\)
2 \(\lambda_{A}=\lambda_{B}\)
3 \(\lambda_{A}=\lambda_{B} \ln 2\)
4 \(\lambda_{A} \ln 2=\lambda_{B}\)
PHXII13:NUCLEI

364035 During mean life of a radioactive element, the fraction that disintegrates is

1 \(\frac{1}{e}\)
2 \(\frac{{e - 1}}{e}\)
3 \(e\)
4 \(\frac{e}{{e - 1}}\)
PHXII13:NUCLEI

364036 If a radioactive element having half-life of \(30\;\min \) is undergoing beta decay, the dfraction of radioactive element remains undecayed after \(90\;\min \) will be

1 \(\dfrac{1}{8}\)
2 \(\dfrac{1}{16}\)
3 \(\dfrac{1}{4}\)
4 \(\dfrac{1}{2}\)
PHXII13:NUCLEI

364037 Decay constants of two radio - active samples \(A\) and \(B\) are 15\(x\) and 3\(x\) respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in \(A\) and \(B\) after a time 1/6\(x\) is

1 \(e\)
2 \({e^2}\)
3 \({e^{ - 1}}\)
4 \({e^{ - 2}}\)
PHXII13:NUCLEI

364034 Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_{A}\) and \(\lambda_{B}\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.

1 \(\lambda_{A}=2 \lambda_{B}\)
2 \(\lambda_{A}=\lambda_{B}\)
3 \(\lambda_{A}=\lambda_{B} \ln 2\)
4 \(\lambda_{A} \ln 2=\lambda_{B}\)
PHXII13:NUCLEI

364035 During mean life of a radioactive element, the fraction that disintegrates is

1 \(\frac{1}{e}\)
2 \(\frac{{e - 1}}{e}\)
3 \(e\)
4 \(\frac{e}{{e - 1}}\)
PHXII13:NUCLEI

364036 If a radioactive element having half-life of \(30\;\min \) is undergoing beta decay, the dfraction of radioactive element remains undecayed after \(90\;\min \) will be

1 \(\dfrac{1}{8}\)
2 \(\dfrac{1}{16}\)
3 \(\dfrac{1}{4}\)
4 \(\dfrac{1}{2}\)
PHXII13:NUCLEI

364037 Decay constants of two radio - active samples \(A\) and \(B\) are 15\(x\) and 3\(x\) respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in \(A\) and \(B\) after a time 1/6\(x\) is

1 \(e\)
2 \({e^2}\)
3 \({e^{ - 1}}\)
4 \({e^{ - 2}}\)
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PHXII13:NUCLEI

364034 Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_{A}\) and \(\lambda_{B}\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.

1 \(\lambda_{A}=2 \lambda_{B}\)
2 \(\lambda_{A}=\lambda_{B}\)
3 \(\lambda_{A}=\lambda_{B} \ln 2\)
4 \(\lambda_{A} \ln 2=\lambda_{B}\)
PHXII13:NUCLEI

364035 During mean life of a radioactive element, the fraction that disintegrates is

1 \(\frac{1}{e}\)
2 \(\frac{{e - 1}}{e}\)
3 \(e\)
4 \(\frac{e}{{e - 1}}\)
PHXII13:NUCLEI

364036 If a radioactive element having half-life of \(30\;\min \) is undergoing beta decay, the dfraction of radioactive element remains undecayed after \(90\;\min \) will be

1 \(\dfrac{1}{8}\)
2 \(\dfrac{1}{16}\)
3 \(\dfrac{1}{4}\)
4 \(\dfrac{1}{2}\)
PHXII13:NUCLEI

364037 Decay constants of two radio - active samples \(A\) and \(B\) are 15\(x\) and 3\(x\) respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in \(A\) and \(B\) after a time 1/6\(x\) is

1 \(e\)
2 \({e^2}\)
3 \({e^{ - 1}}\)
4 \({e^{ - 2}}\)