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:
1 x 10¹⁷
Explanation:
Given data:
Radius of the earth = 6000km
Radius of an atom = 60pm
Now, how many orders is the radius of the earth larger than an atom
Solution:
To solve this problem, let us express both quantity as the same unit;
1000m = 1km
6000km = 6000 x 10³m = 6 x 10⁶m
60pm;
1 x 10⁻¹²m = 1pm
60pm = 60 x 1 x 10⁻¹²m = 6 x 10⁻¹¹m
Now;
The order: 
= 1 x 10¹⁷
Answer:
(B) The wavelength that a star radiates the most energy is inversely proportional to the temperature.
Explanation:
As we know that
According to Wien's law wavelength is inverse proportional to the temperature .
λ.T = Constant.
λ.∝ 1 /T
As we know that star radiates wavelength and this wavelength is inverse proportional to the temperature of the star.
The temperature of cool star is cooler than the temperature of hot star that is cool star looks red and hot star looks blue.Cool star have low energy and hot star have high energy.
So option B is correct.
(B) The wavelength that a star radiates the most energy is inversely proportional to the temperature.
Answer:
Explanation:
The horizontal distance covered by the ball in the falling is only determined by its horizontal motion - in fact, it is given by
where
is the horizontal velocity
t is the time of flight
The time of flight, instead, is only determined by the vertical motion of the ball: however, in this problem the vertical velocity is not changed (it is zero in both cases), so the time of flight remains the same.
In the first situation, the horizontal distance covered is
in the second case, the horizontal velocity is increased to
And so the new distance travelled will be
So, the distance increases linearly with the horizontal velocity.
Answer:
Two marbles are launched at t = 0 in the experiment illustrated in the figure below. Marble 1 is launched horizontally with a speed of 4.20 m/s from a height h = 0.950 m. Marble 2 is launched from ground level with a speed of 5.94 m/s at an angle above the horizontal. (a) Where would the marbles collide in the absence of gravity? Give the x and y coordinates of the collision point. (b) Where do the marbles collide given that gravity produces a downward acceleration of g = 9.81 m/s2? Give the x and y coordinates.
Explanation:
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