91影视

When an unstable nucleus accepts an electron, the phenomena is known as electron capture. The electron combines with a proton to change into a neutron. The result of electron capture is that the daughter nucleus formed has the same mass number but the atomic number decreases by one unit.

${}_1{}^{1}p+{}_{-1}{}^{0}e鈫�{}_0{}^{1}n$

The ${}_{86}{}^{210}Rn$ decays by capturing an electron to form ${}_{85}{}^{210}At$. The equation representing the decay is given below.

${}_{86}{}^{210}Rn{+}_{-1}^{0}e{鈫�}_{85}^{210}At$

In the problem, it state that ${}_{86}{}^{210}Rnemits2.368MeV$. The energy can be converted into atomic mass units with the help of the following conversion relations.

$$\begin{gathered} 1amu=931.5x{10}^{6}eV=931.5MeV \\ 2.368MeV=2.368鈥�MeV\left(\frac{1amu}{931.5MeV}\right)=0.0025amu \end{gathered}$$

We will use to calculate the isotopic mass,

$$\begin{gathered} Mas{s}_{85}^{210}At=Mas{s}_{86}^{210}Rn+massofelectron-equivalent \\ Mas{s}_{85}^{210}At=209.9897amu+0.000549amu-0.0025amu \\ Mas{s}_{85}^{210}At=209.9927amu \end{gathered}$$

Therefore, the required value of $Mas{s}_{85}^{210}At=209.9927amu$.