364017
Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half-life of 1 year. After 1 year
1 All the containers will contain the same number of atoms of the material but that number will only be approximately 5000.
2 The containers will in general have different numbers of the atoms of the material but their average will be close to 5000.
3 All the containers will have 5000 atoms of the materials.
4 None of the containers can have more than 5000 atoms.
Explanation:
Radioactivity is spontaneous activity of the radioactive material. In \(t = 1\) year \( = \) half-life of material; on the average, half the number of atoms will decay. Therefore, the containers will in general have different number of atoms of the material, but their average will be close to 5000.
NCERT Exemplar
PHXII13:NUCLEI
364018
Assertion : If the half-life of a radioactive substance is 40 days then 25% substance decays in 20 days Reason : \(N = {N_0}{\left( {\frac{1}{2}} \right)^n}\)
1 Both assertion and reason are correct and reason is the correct explanation of assertion.
2 Both assertion and reason are correct but reason is not the correct explanation of assertion.
3 Assertion is correct but reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In 20 days 50% of the substance decays. \(N = \frac{{{N_0}}}{{{2^n}}}\) option (4) is correct
PHXII13:NUCLEI
364019
The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half - life of the radioactive sample is
1 \(\frac{1}{4}\)
2 \(\frac{1}{{2\sqrt 2 }}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{{\sqrt 2 }}\)
Explanation:
\({N_0}\) is the initial number of radioactive nuclei and \(N\) is the number of nuclei that remains undecayed. Thus, \(\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n}\) where \(n\) is the number of half lives As \(n = \frac{t}{{{T_{1/2}}}} = \frac{{\frac{1}{2}{T_{1/2}}}}{{{T_{1/2}}}} = \frac{1}{2}\) \(\therefore \frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^{1/2}} = \frac{1}{{\sqrt 2 }}\)
KCET - 2011
PHXII13:NUCLEI
364020
Assertion : Radioactivity of \(10^{8}\) undecayed radioactive nuclei of half life of 50 days is equal to that of \(1.2 \times 10^{8}\) number of undecayed nuclei of some other material with half life of 60 days Reason : Radioactivity is proportional to half-life.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
As the radioactivity is indeed proportional to the number of undecayed nuclei. \(A=\) Activity \(=\lambda N=\left(\dfrac{0.693}{T_{1 / 2}}\right) N\) \(\Rightarrow A \propto \dfrac{1}{\left(T_{1 / 2}\right)}\) \(\Rightarrow A\) is not proportional to \(T_{1 / 2}\) \(\Rightarrow\) Reason is false But for one sample, \(T_{1 / 2}=50\) days, \(N=10^{8}\) For the other sample, \(T_{1 / 2}=60\) days, \(N=1.2 \times 10^{8}\) \(\Rightarrow\) If \(A\) is same, \(\left(\dfrac{N}{T_{1 / 2}}\right)\) shall be equal. It is so as: \(\left(\dfrac{10^{8}}{50}\right)=\left(\dfrac{1.2 \times 10^{8}}{60}\right)=0.02\) \(\Rightarrow\) Assertion is true So correct option is (3).
364017
Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half-life of 1 year. After 1 year
1 All the containers will contain the same number of atoms of the material but that number will only be approximately 5000.
2 The containers will in general have different numbers of the atoms of the material but their average will be close to 5000.
3 All the containers will have 5000 atoms of the materials.
4 None of the containers can have more than 5000 atoms.
Explanation:
Radioactivity is spontaneous activity of the radioactive material. In \(t = 1\) year \( = \) half-life of material; on the average, half the number of atoms will decay. Therefore, the containers will in general have different number of atoms of the material, but their average will be close to 5000.
NCERT Exemplar
PHXII13:NUCLEI
364018
Assertion : If the half-life of a radioactive substance is 40 days then 25% substance decays in 20 days Reason : \(N = {N_0}{\left( {\frac{1}{2}} \right)^n}\)
1 Both assertion and reason are correct and reason is the correct explanation of assertion.
2 Both assertion and reason are correct but reason is not the correct explanation of assertion.
3 Assertion is correct but reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In 20 days 50% of the substance decays. \(N = \frac{{{N_0}}}{{{2^n}}}\) option (4) is correct
PHXII13:NUCLEI
364019
The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half - life of the radioactive sample is
1 \(\frac{1}{4}\)
2 \(\frac{1}{{2\sqrt 2 }}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{{\sqrt 2 }}\)
Explanation:
\({N_0}\) is the initial number of radioactive nuclei and \(N\) is the number of nuclei that remains undecayed. Thus, \(\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n}\) where \(n\) is the number of half lives As \(n = \frac{t}{{{T_{1/2}}}} = \frac{{\frac{1}{2}{T_{1/2}}}}{{{T_{1/2}}}} = \frac{1}{2}\) \(\therefore \frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^{1/2}} = \frac{1}{{\sqrt 2 }}\)
KCET - 2011
PHXII13:NUCLEI
364020
Assertion : Radioactivity of \(10^{8}\) undecayed radioactive nuclei of half life of 50 days is equal to that of \(1.2 \times 10^{8}\) number of undecayed nuclei of some other material with half life of 60 days Reason : Radioactivity is proportional to half-life.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
As the radioactivity is indeed proportional to the number of undecayed nuclei. \(A=\) Activity \(=\lambda N=\left(\dfrac{0.693}{T_{1 / 2}}\right) N\) \(\Rightarrow A \propto \dfrac{1}{\left(T_{1 / 2}\right)}\) \(\Rightarrow A\) is not proportional to \(T_{1 / 2}\) \(\Rightarrow\) Reason is false But for one sample, \(T_{1 / 2}=50\) days, \(N=10^{8}\) For the other sample, \(T_{1 / 2}=60\) days, \(N=1.2 \times 10^{8}\) \(\Rightarrow\) If \(A\) is same, \(\left(\dfrac{N}{T_{1 / 2}}\right)\) shall be equal. It is so as: \(\left(\dfrac{10^{8}}{50}\right)=\left(\dfrac{1.2 \times 10^{8}}{60}\right)=0.02\) \(\Rightarrow\) Assertion is true So correct option is (3).
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXII13:NUCLEI
364017
Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half-life of 1 year. After 1 year
1 All the containers will contain the same number of atoms of the material but that number will only be approximately 5000.
2 The containers will in general have different numbers of the atoms of the material but their average will be close to 5000.
3 All the containers will have 5000 atoms of the materials.
4 None of the containers can have more than 5000 atoms.
Explanation:
Radioactivity is spontaneous activity of the radioactive material. In \(t = 1\) year \( = \) half-life of material; on the average, half the number of atoms will decay. Therefore, the containers will in general have different number of atoms of the material, but their average will be close to 5000.
NCERT Exemplar
PHXII13:NUCLEI
364018
Assertion : If the half-life of a radioactive substance is 40 days then 25% substance decays in 20 days Reason : \(N = {N_0}{\left( {\frac{1}{2}} \right)^n}\)
1 Both assertion and reason are correct and reason is the correct explanation of assertion.
2 Both assertion and reason are correct but reason is not the correct explanation of assertion.
3 Assertion is correct but reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In 20 days 50% of the substance decays. \(N = \frac{{{N_0}}}{{{2^n}}}\) option (4) is correct
PHXII13:NUCLEI
364019
The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half - life of the radioactive sample is
1 \(\frac{1}{4}\)
2 \(\frac{1}{{2\sqrt 2 }}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{{\sqrt 2 }}\)
Explanation:
\({N_0}\) is the initial number of radioactive nuclei and \(N\) is the number of nuclei that remains undecayed. Thus, \(\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n}\) where \(n\) is the number of half lives As \(n = \frac{t}{{{T_{1/2}}}} = \frac{{\frac{1}{2}{T_{1/2}}}}{{{T_{1/2}}}} = \frac{1}{2}\) \(\therefore \frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^{1/2}} = \frac{1}{{\sqrt 2 }}\)
KCET - 2011
PHXII13:NUCLEI
364020
Assertion : Radioactivity of \(10^{8}\) undecayed radioactive nuclei of half life of 50 days is equal to that of \(1.2 \times 10^{8}\) number of undecayed nuclei of some other material with half life of 60 days Reason : Radioactivity is proportional to half-life.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
As the radioactivity is indeed proportional to the number of undecayed nuclei. \(A=\) Activity \(=\lambda N=\left(\dfrac{0.693}{T_{1 / 2}}\right) N\) \(\Rightarrow A \propto \dfrac{1}{\left(T_{1 / 2}\right)}\) \(\Rightarrow A\) is not proportional to \(T_{1 / 2}\) \(\Rightarrow\) Reason is false But for one sample, \(T_{1 / 2}=50\) days, \(N=10^{8}\) For the other sample, \(T_{1 / 2}=60\) days, \(N=1.2 \times 10^{8}\) \(\Rightarrow\) If \(A\) is same, \(\left(\dfrac{N}{T_{1 / 2}}\right)\) shall be equal. It is so as: \(\left(\dfrac{10^{8}}{50}\right)=\left(\dfrac{1.2 \times 10^{8}}{60}\right)=0.02\) \(\Rightarrow\) Assertion is true So correct option is (3).
364017
Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half-life of 1 year. After 1 year
1 All the containers will contain the same number of atoms of the material but that number will only be approximately 5000.
2 The containers will in general have different numbers of the atoms of the material but their average will be close to 5000.
3 All the containers will have 5000 atoms of the materials.
4 None of the containers can have more than 5000 atoms.
Explanation:
Radioactivity is spontaneous activity of the radioactive material. In \(t = 1\) year \( = \) half-life of material; on the average, half the number of atoms will decay. Therefore, the containers will in general have different number of atoms of the material, but their average will be close to 5000.
NCERT Exemplar
PHXII13:NUCLEI
364018
Assertion : If the half-life of a radioactive substance is 40 days then 25% substance decays in 20 days Reason : \(N = {N_0}{\left( {\frac{1}{2}} \right)^n}\)
1 Both assertion and reason are correct and reason is the correct explanation of assertion.
2 Both assertion and reason are correct but reason is not the correct explanation of assertion.
3 Assertion is correct but reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In 20 days 50% of the substance decays. \(N = \frac{{{N_0}}}{{{2^n}}}\) option (4) is correct
PHXII13:NUCLEI
364019
The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half - life of the radioactive sample is
1 \(\frac{1}{4}\)
2 \(\frac{1}{{2\sqrt 2 }}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{{\sqrt 2 }}\)
Explanation:
\({N_0}\) is the initial number of radioactive nuclei and \(N\) is the number of nuclei that remains undecayed. Thus, \(\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n}\) where \(n\) is the number of half lives As \(n = \frac{t}{{{T_{1/2}}}} = \frac{{\frac{1}{2}{T_{1/2}}}}{{{T_{1/2}}}} = \frac{1}{2}\) \(\therefore \frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^{1/2}} = \frac{1}{{\sqrt 2 }}\)
KCET - 2011
PHXII13:NUCLEI
364020
Assertion : Radioactivity of \(10^{8}\) undecayed radioactive nuclei of half life of 50 days is equal to that of \(1.2 \times 10^{8}\) number of undecayed nuclei of some other material with half life of 60 days Reason : Radioactivity is proportional to half-life.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
As the radioactivity is indeed proportional to the number of undecayed nuclei. \(A=\) Activity \(=\lambda N=\left(\dfrac{0.693}{T_{1 / 2}}\right) N\) \(\Rightarrow A \propto \dfrac{1}{\left(T_{1 / 2}\right)}\) \(\Rightarrow A\) is not proportional to \(T_{1 / 2}\) \(\Rightarrow\) Reason is false But for one sample, \(T_{1 / 2}=50\) days, \(N=10^{8}\) For the other sample, \(T_{1 / 2}=60\) days, \(N=1.2 \times 10^{8}\) \(\Rightarrow\) If \(A\) is same, \(\left(\dfrac{N}{T_{1 / 2}}\right)\) shall be equal. It is so as: \(\left(\dfrac{10^{8}}{50}\right)=\left(\dfrac{1.2 \times 10^{8}}{60}\right)=0.02\) \(\Rightarrow\) Assertion is true So correct option is (3).