Select the correct answer. Which missing item would complete this alpha decay reaction? (}_{100)^257Fmarrow +_(2)^4He A. (}_{98)^253Cf B. (}_{96)^255Cm C. (}_{98)^253Fm D. (}_{90)^232Th E. (}_{92)^288U

## Step 1: <br />Alpha decay is a type of radioactive decay where an atomic nucleus emits an alpha particle (consisting of 2 protons and 2 neutrons) and transforms into a new element. The general formula for alpha decay is:<br /><br />### \[ {}_{Z}^{A}X \rightarrow {}_{Z-2}^{A-4}Y + {}_{2}^{4}He \]<br /><br />where \(Z\) is the atomic number, \(A\) is the mass number, \(X\) is the parent nucleus, \(Y\) is the daughter nucleus, and \({}_{2}^{4}He\) is the alpha particle.<br /><br />## Step 2:<br />In the given reaction, \({}_{100}^{257}Fm\) (Fermium) undergoes. According to the alpha decay formula, the daughter nucleus will have an atomic number 2 less than Fermium and a mass number 4 less than Fermium.<br /><br />## Step 3:<br />Calculating the atomic number of the daughter nucleus:<br /><br />### \[ Z_{daughter} = Z_{Fermium} - 2 = 100 - 2 = 98 \]<br /><br />## Step 4:<br />Calculating the mass number of the daughter nucleus:<br /><br />### \[ A_{daughter} = A_{Fermium} - 4 = 257 - 4 = 253 \]<br /><br />## Step 5:<br />The element with atomic number 98 is Californium (Cf). Therefore, the missing item in the reaction is \({}_{98}^{253}Cf\).