How long will it take for 100 grams of a substance with a half-life of 2 years to decay to a mass of 50 grams?

2 years to decay to a mass of 50g.

Explanation:

given:

100g of substance with a half life of 2 years

to a mass of 50g

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

                          ln 2             0.693

Half life T1/2 =  =  

                              λ                  λ

where  λ = rate constant

The initial amount of 100 grams is decaying to a mass of 50 grams is half of its initial value.

Therefore, it will take 2 years for the decay.

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

b is the correct answer

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