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Question:

After the emission of one α-particle followed by two β- particles from 23892U, the number of neutrons in the newly formed nucleus is

142

140

144

146

Solution:

The emission of one α-particle reduces the mass number by 4 and the atomic number by 2. The emission of one β-particle increases the atomic number by 1 and leaves the mass number unchanged.

Initially, 23892U has 238 - 92 = 146 neutrons.

After emission of one α-particle:
Mass number = 238 - 4 = 234
Atomic number = 92 - 2 = 90
Number of neutrons = 234 - 90 = 144

After emission of two β-particles:
Mass number = 234 (unchanged)
Atomic number = 90 + 1 + 1 = 92
Number of neutrons = 234 - 92 = 142

Therefore, the number of neutrons in the newly formed nucleus is 142.