A uranium 238 atom travels toward the right with an initial speed of 50.0 km/s a

Question

A uranium 238 atom travels toward the right with an initial speed of 50.0 km/s and a mass of 238u. It spontaneously dedcays by ejecting an alpha particle (2 protons, 2 neutrons) at a speed of 1.50x10^4km/s to the right and has a mass of 4u. What is the final velocity of the rermaining nucleus, thorium-234, with a mass of 234u? (no need to convert the masses to kg).

There are multiple answers to this question floating around Chegg for some particular reason. When you answer this would you mind including energy bar graphs to help me visualize the situation an stating what equations you are using before solving the problem? Thanks.

Explanation / Answer

Mass of U-238 is m = 238 u

Mass of alpha particle m ' = 4 u

Mass of thorium M = 234 u

Initial speed of U-238 is u = 50 km/s

Speed of alpha particle u ' = 1.5 x10 4 km/s

Speed of thorium U = ?

From law of conservation of linear momentum,

mu = m ' u ' + MU

(238 x 50 ) = ( 4 x 1.5 x10 4 ) + (234 U )

11900 = 60000 +234 U

234 U = - 48100

U = - 48100 /234

U = -205.55 km/s

negative sign indicates moving towards LEFT.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.