$[$Maximum mark: $7]$

$18$M$\mathrm{.}25$L$.$TZ$1\mathrm{.}6$

The radioactive nuclide beryllium$-10($Be$-10)$ undergoes beta minus $($ decay to form a stable boron $($B$)$ nuclide.

$($a$)$ Identify the missing information for this decay.

$[1]$

The initial number of nuclel in a pure sample of beryllium$-10$ is $N_0.$ The graph shows how the number of remaining beryllium nudei in the sample varies with time,

sample varies with time.

$[2]$

$($bil$)$ After $4\mathrm{.}3{10}^6$ years.

number of prodiced boron nuclei

number of remaining beryllium nuclei $=7.$

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

$(3)$

$($biii$)$ Berylium$-10$ is used to investigate ice samples from Antarctica.

A sample of ice initially contains $7\mathrm{.}6{10}^{11}$ atoms of beryllium$-$

State the number of remaining beryllium$-10$ nuclei in the sample after $2\mathrm{.}8{10}^6$ years.