A freshly prepared sample of radioactive isotope has an activity of 10 mCi. After 4 hours, its activity is 8 mCi. Find: (a) the decay constant  and half-life T1/2; (b) How many atoms of the isotope were contained in the freshly prepared sample? (c) What is the sample's activity 30 hours after it is prepared?

(a). The decay constant is

The half life is 11.3 hr.

(b). The value of N₀ is

(c). The sample's activity is 1.87 mCi.

Explanation:

Given that,

Activity

Time

Activity R= 8 mCi

(a). We need to calculate the decay constant

Using formula of activity

Put the value into the formula

We need to calculate the half life

Using formula of half life

Put the value into the formula

(b). We need to calculate the value of N₀

Using formula of

Put the value into the formula

(c). We need to calculate the sample's activity

Using formula of activity

Put the value intyo the formula

Hence, (a). The decay constant is

The half life is 11.3 hr.

(b). The value of N₀ is

(c). The sample's activity is 1.87 mCi.

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

like poles repel so keep pushing north to north and repels funny to see this