The bubbles in a carbonated soft drink are produced when carbonic acid decomposes to form carbon dioxide and water. In a closed
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Answer:
- <u><em>(b) 1:1</em></u>
Explanation:
<u></u>
<u>1. Formulae:</u>
- E = hf
- E = h.v/λ
- λ = h/(mv)
- E = (1/2)mv²
Where:
- E = kinetic energy of the particle
- λ = de-Broglie wavelength
- m = mass of the particle
- v = speed of the particle
- h = Planck constant
<u><em>2. Reasoning</em></u>
An alha particle contains 2 neutrons and 2 protons, thus its mass number is 4.
A proton has mass number 1.
Thus, the relative masses of an alpha particle and a proton are:
For the kinetic energies you find:
Thus:
From de-Broglie equation, λ = h/(mv)
The equation of motion of a pendulum is:
where it its length and
is the gravitational acceleration. Notice that the mass is absent from the equation! This is quite hard to solve, but for <em>small</em> angles (
), we can use:
Additionally, let us define:
We can now write:
The solution to this differential equation is:
where and
are constants to be determined using the initial conditions. Notice that they will not have any influence on the period, since it is given simply by:
This justifies that the period depends only on the pendulum's length.