The half-life of a certain element is 100 days. How many half-lives will it be before only one-eighth of this element remains?
1 answer:
Answer:
3
Explanation:
The half-life is the time it takes for the amount of radioactive isotope to halve. Therefore, we have:
- After 1 half-life, only 1/2 of the element will be left
- After 2 half-lives, only 1/4 of the element will be left
- After 3 half-lives, only 1/8 of the element will be left
So, it will take 3 half-lives for the element to become 1/8 of its original amount.
Mathematically, this can be also verified by using the equation
where
N(t) is the amount of the element left at time t
N0 is the initial amount of the element
is the half-life
Substituting (3 half-lives), we find
You might be interested in
Answer:
the force P required for impending motion is 132.3 N
the largest value of "h" allowed if the cabinet is not to tip over is 0.8 m
Explanation:
Given that:
mass of the cabinet m = 45 kg
coefficient of static friction μ = 0.30
A free flow body diagram illustrating what the question represents is attached in the file below;
The given condition from the question let us realize that ; the casters are locked to prevent the tires from rotating.
Thus; considering the forces along the vertical axis ; we have :
The upward force and the downward force is :
where;
are the normal contact force at center point A and B respectively .
------- equation (1)
Considering the forces on the horizontal axis:
where ;
are the static friction at center point A and B respectively.
which can be written also as:
replacing our value from equation (1)
P = 0.30 ( 441)
P = 132.3 N
Thus; the force P required for impending motion is 132.3 N
b) Since the horizontal distance between the casters A and B is 480 mm; Then half the distance = 480 mm/2 = 240 mm = 0.24 cm
the largest value of "h" allowed for the cabinet is not to tip over is calculated by determining the limiting condition of the unbalanced torque whose effect is canceled by the normal reaction at and it is shifted to
:
Then:
h = 0.8 m
Thus; the largest value of "h" allowed if the cabinet is not to tip over is 0.8 m
