22P2Q06

6a)

Average time taken for the activity of a sample of the radioactive isotope to halve.

OR

The average time taken for the number of undecayed nuclei to decrease by half.

6b)

A steep gradient implies a large activity. If the activity is large, the fractional error caused by background radiation is smaller.

6c)

Before the decay, total momentum of the system is zero. By PCOM, the total momentum must remain as zero after the emission.

Since the beta particle’s momentum is not opposite in direction to the recoiling nucleus, there must be a third momentum carried by a third particle in order for the total momentum to be zero.

6di)

\displaystyle {}_{38}^{90}Sr\to {}_{-1}^{0}\beta +{}_{39}^{90}Y

6dii)

Since \displaystyle A=\lambda N, the gradient of the A-N graph is the decay constant.

\displaystyle \lambda =\frac{4.6\times {{10}^{9}}}{6.0\times {{10}^{18}}}=7.677\times {{10}^{-10}}\text{ }{{\text{s}}^{-1}}

\displaystyle {{t}_{\frac{1}{2}}}=\frac{\ln 2}{\lambda }=\frac{\ln 2}{7.667\times {{10}^{-10}}}=9.04\times {{10}^{8}}\text{ s}

6e)

\displaystyle \frac{N}{{{N}_{0}}}={{(\frac{1}{2})}^{3.5}}=0.088388

\displaystyle \text{Ratio }=\frac{\text{Number of undecayed}}{\text{Number of decayed}}=\frac{0.088388}{(1-0.088388)}=0.0970

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