Cerium-143 is a radioactive isotope that decays to produce praseodymium-143. The half-life for cerium-143 is approximately 33 hours. If 12.5 g cerium-143 remains from a 100-g sample, which statement is true? Select all that apply. A.
Cerium-143 decayed for 132 hours.

B.
Cerium-143 decayed for 99 hours.

C.
Four half-lives have passed.

D.
Three half-lives have passed.

E.
Cerium-143 decayed for 166 hours.

F.
Two half-lives have passed.

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first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j

the answer is d.) potassium