1) The half-life is the time required for a substance to reduce to half its initial value. In formulas:
(1)
where
m(t) is the amount of substance left at time t
m0 is the initial mass
is the half-life
In this problem, the half-life of the substance is 20 years:
therefore, the fraction of sample left after t=40 years will be
So, only 1/4 of the original sample will be left, which corresponds to 25%.
2) We can use again formula (1), by re-arranging it:
If we use m(t)=10 g (mass of uranium left at time t), and
(the time is equal to 4 half lifes), we get
So, the initial sample of uranium was 160 g.
Answer:
thickness t = 528.433 nm
Explanation:
given data
wavelength λ1 = 477.1 nm
wavelength λ2 = 668.0 nm
n = 1.58
solution
we know for constructive interference condition will be
2 × t × μ = (m1+0.5) × λ1 ....................1
2 × t × μ = (m2+0.5) × λ2 ....................2
so we can say from equation 1 and 2
(m1+0.5) × λ1 = (m2+0.5) × λ2
so
..............3
put here value and we get
= 1.4
...................4
so we here from equation 4
m1+0.5 = 7
m1 = 3 .................5
m2+0.5 = 4
m2 = 2 .................6
so now put value in equation 1
2 × t × μ = (m1+0.5) × λ1
2 × t × 1.58 = (3+0.5) × 477.1
solve it we get
thickness t = 528.433 nm
Answer:
C) 16.3 ml
Explanation:
Density is equal to the ratio between the mass of an object and its volume:
where
m is the mass
V is the volume
In our problem, we know:
- density of aluminium: 
- mass of the aluminium foil: 
So we can re-arrange the equation above and use these data to find the volume of the piece of aluminium foil:
Answer:
The magnitude and direction of the resultant force are approximately 599.923 newtons and 36.405°.
Explanation:
First, we must calculate the resultant force (
), in newtons, by vectorial sum:
![\vec F = [(-200\,N)\cdot \cos 60^{\circ}+(400\,N)\cdot \cos 45^{\circ}+300\,N]\,\hat{i} + [(200\,N)\cdot \sin 60^{\circ} + (400\,N)\cdot \sin 45^{\circ}-100\,N]\,\hat{j}](https://tex.z-dn.net/?f=%5Cvec%20F%20%3D%20%5B%28-200%5C%2CN%29%5Ccdot%20%5Ccos%2060%5E%7B%5Ccirc%7D%2B%28400%5C%2CN%29%5Ccdot%20%5Ccos%2045%5E%7B%5Ccirc%7D%2B300%5C%2CN%5D%5C%2C%5Chat%7Bi%7D%20%2B%20%5B%28200%5C%2CN%29%5Ccdot%20%5Csin%2060%5E%7B%5Ccirc%7D%20%2B%20%28400%5C%2CN%29%5Ccdot%20%5Csin%2045%5E%7B%5Ccirc%7D-100%5C%2CN%5D%5C%2C%5Chat%7Bj%7D)
(1)
Second, we calculate the magnitude of the resultant force by Pythagorean Theorem:
Let suppose that direction of the resultant force is an standard angle. According to (1), the resultant force is set in the first quadrant:
Where 
is the direction of the resultant force, in sexagesimal degrees.
The magnitude and direction of the resultant force are approximately 599.923 newtons and 36.405°.
