Questions: Identify the missing element in the reaction below. [ 92^235 U+0^1 n rightarrow 35^95 Br+?+20^1 n ] 92^140 U 57^140 La 57^139 La 57^141 La

Transcript text: Identify the missing element in the reaction below. \[ { }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{35}^{95} \mathrm{Br}+?+2{ }_{0}^{1} \mathrm{n} \] ${ }_{92}^{140} \mathrm{U}$ ${ }_{57}^{140} \mathrm{La}$ ${ }_{57}^{139} \mathrm{La}$ ${ }_{57}^{141} \mathrm{La}$

Solution

Solution Steps

Step 1: Write the Nuclear Reaction Equation

The given nuclear reaction is: \[ {}_{92}^{235} \mathrm{U} + {}_{0}^{1} \mathrm{n} \rightarrow {}_{35}^{95} \mathrm{Br} + ? + 2{}_{0}^{1} \mathrm{n} \]

Step 2: Determine the Missing Element's Mass Number

The mass number (A) must be conserved in the reaction. The sum of the mass numbers on the left side must equal the sum of the mass numbers on the right side.

On the left side: \[ 235 + 1 = 236 \]

On the right side: \[ 95 + A + 2 \times 1 = 95 + A + 2 \]

Equating both sides: \[ 236 = 95 + A + 2 \] \[ 236 = 97 + A \] \[ A = 236 - 97 \] \[ A = 139 \]

Step 3: Determine the Missing Element's Atomic Number

The atomic number (Z) must also be conserved. The sum of the atomic numbers on the left side must equal the sum of the atomic numbers on the right side.

On the left side: \[ 92 + 0 = 92 \]

On the right side: \[ 35 + Z + 2 \times 0 = 35 + Z \]

Equating both sides: \[ 92 = 35 + Z \] \[ Z = 92 - 35 \] \[ Z = 57 \]

Step 4: Identify the Missing Element

The element with atomic number 57 is Lanthanum (La). Therefore, the missing element is: \[ {}_{57}^{139} \mathrm{La} \]