Answer: a) 3.85 days
b) 10.54 days
Explanation:-
Expression for rate law for first order kinetics is given by:
where,
k = rate constant = ?
t = time taken for decomposition = 3 days
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = 
First we have to calculate the rate constant, we use the formula :
Now put all the given values in above equation, we get
a) Half-life of radon-222:
Thus half-life of radon-222 is 3.85 days.
b) Time taken for the sample to decay to 15% of its original amount:
where,
k = rate constant = 
t = time taken for decomposition = ?
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = 
Thus it will take 10.54 days for the sample to decay to 15% of its original amount.
Answer:
Voltage in primary coil is 3.91 V
Explanation:
For transformer we know that the working principle is given as
here we know that
![V_1 [tex] = voltage in primary coil[tex]V_2 = 25 V](https://tex.z-dn.net/?f=V_1%20%5Btex%5D%20%3D%20voltage%20in%20primary%20coil%3C%2Fp%3E%3Cp%3E%5Btex%5DV_2%20%3D%2025%20V)
Now we have
We want to find how much momentum the dumbbell has at the moment it strikes the floor. Let's use this kinematics equation:
Vf² = Vi² + 2ad
Vf is the final velocity of the dumbbell, Vi is its initial velocity, a is its acceleration, and d is the height of its fall.
Given values:
Vi = 0m/s (dumbbell starts falling from rest)
a = 10m/s² (we'll treat downward motion as positive, this doesn't affect the result as long as we keep this in mind)
d = 80×10⁻²m
Plug in the values and solve for Vf:
Vf² = 2(10)(80×10⁻²)
Vf = ±4m/s
Reject the negative root.
Vf = 4m/s
The momentum of the dumbbell is given by:
p = mv
p is its momentum, m is its mass, and v is its velocity.
Given values:
m = 10kg
v = 4m/s (from previous calculation)
Plug in the values and solve for p:
p = 10(4)
p = 40kg×m/s
the answer is (a) molecules
