$[$Maximum mark: $7]$

$12$M$2$sitzi$\mathrm{.}6$

The radioactive nudide berylium$-10($Be$-10)$ undergoes beta minus $(9-)$ decay to forma stable boron $($t$)$ nuclide.

$($a$)$ Dentify the missing information forthis decay.

$3407B^B,n*0$

$[1]$

The inital number of nuclel in a pure sample of beryllum$-10$ is $N_0.$ The graph shows how the number of remaining beryllium nuclei in the smple varies with time.

$($bi$)$ On the graph, sketh how the rumber of boron nuclei in the sample varies with time.

$[2]$

$($b$.$ii$)$ After $4\mathrm{.}3{10}^6$ years;

number of produced boron nuclei number of remaining beryllium nuclei $=7.$

Show that the half life of berylium$-10$ is $1\mathrm{.}4{10}^6$ years.

$[3]$

$($biii$)$ Beylium$-10$ is used to investigate ice samplesfrom Antarctica. A sample of ice initially contains $7\mathrm{.}6{10}^{11}$ atoms of beryllum$10.$ State the number of remaining beylitum$-10$ nuclei in the sample after $28{10}^{\text{'}}$ years.