364001
The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is
364003
In a radioactive disintegrations, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is
1 \(1/{e^2}\)
2 \(1/e\)
3 \(e\)
4 \({e^2}\)
Explanation:
Let the initial number of atoms at time \(t = 0\) be \({N_0}\). Let the number of atoms at any instant of time \(t\) be \(N\). According to radioactive decay law, \(N = {N_0}{e^{ - \lambda t}}\) Mean life \(\tau = 1/\lambda \), where \(\lambda \) is the decay constant here \(t = \tau \) (given) \(\therefore N = {N_0}{e^{ - \frac{1}{\tau } \times \tau }}\) or \(N = {N_0}{e^{ - 1}}\) or \(\frac{{{N_0}}}{N} = e\)
364001
The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is
364003
In a radioactive disintegrations, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is
1 \(1/{e^2}\)
2 \(1/e\)
3 \(e\)
4 \({e^2}\)
Explanation:
Let the initial number of atoms at time \(t = 0\) be \({N_0}\). Let the number of atoms at any instant of time \(t\) be \(N\). According to radioactive decay law, \(N = {N_0}{e^{ - \lambda t}}\) Mean life \(\tau = 1/\lambda \), where \(\lambda \) is the decay constant here \(t = \tau \) (given) \(\therefore N = {N_0}{e^{ - \frac{1}{\tau } \times \tau }}\) or \(N = {N_0}{e^{ - 1}}\) or \(\frac{{{N_0}}}{N} = e\)
364001
The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is
364003
In a radioactive disintegrations, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is
1 \(1/{e^2}\)
2 \(1/e\)
3 \(e\)
4 \({e^2}\)
Explanation:
Let the initial number of atoms at time \(t = 0\) be \({N_0}\). Let the number of atoms at any instant of time \(t\) be \(N\). According to radioactive decay law, \(N = {N_0}{e^{ - \lambda t}}\) Mean life \(\tau = 1/\lambda \), where \(\lambda \) is the decay constant here \(t = \tau \) (given) \(\therefore N = {N_0}{e^{ - \frac{1}{\tau } \times \tau }}\) or \(N = {N_0}{e^{ - 1}}\) or \(\frac{{{N_0}}}{N} = e\)
364001
The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is
364003
In a radioactive disintegrations, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is
1 \(1/{e^2}\)
2 \(1/e\)
3 \(e\)
4 \({e^2}\)
Explanation:
Let the initial number of atoms at time \(t = 0\) be \({N_0}\). Let the number of atoms at any instant of time \(t\) be \(N\). According to radioactive decay law, \(N = {N_0}{e^{ - \lambda t}}\) Mean life \(\tau = 1/\lambda \), where \(\lambda \) is the decay constant here \(t = \tau \) (given) \(\therefore N = {N_0}{e^{ - \frac{1}{\tau } \times \tau }}\) or \(N = {N_0}{e^{ - 1}}\) or \(\frac{{{N_0}}}{N} = e\)
