We can solve the problem by using Snell's law, which states
where
is the refractive index of the first medium
is the angle of incidence
is the refractive index of the second medium
is the angle of refraction
In our problem,
(refractive index of air),
and
(refractive index of carbon disulfide), therefore we can re-arrange the previous equation to calculate the angle of refraction:
From which we find
Answer:
ω = √(2T / (mL))
Explanation:
(a) Draw a free body diagram of the mass. There are two tension forces, one pulling down and left, the other pulling down and right.
The x-components of the tension forces cancel each other out, so the net force is in the y direction:
∑F = -2T sin θ, where θ is the angle from the horizontal.
For small angles, sin θ ≈ tan θ.
∑F = -2T tan θ
∑F = -2T (Δy / L)
(b) For a spring, the restoring force is F = -kx, and the frequency is ω = √(k/m). (This is derived by solving a second order differential equation.)
In this case, k = 2T/L, so the frequency is:
ω = √((2T/L) / m)
ω = √(2T / (mL))
The radioactive isotope that would take the least amount of time to become stable is rubidium-91. This is because this isotope is the most stable compared to the rest. This was determined by subtracting its atomic mass by its atomic number. The isotope with the least number of difference is the most stable, while the one with the greatest difference is the most unstable.
Difference:
Rubidium: 54 (most stable)
Iodine: 78
Cesium: 80
Uranium: 146 (least stable)
The statements that apply in this case are:
They show the elements that make up a compound.
They show the types of atoms that make up a molecule.
They show the number of each type of atom in a molecule.
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