Why is there two π in the formula of a mathematical pendulum (T=2π √l/g)?
1 answer:
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Answer:
a. speed, v = 0.97 c
b. time, t' = 20.56 years
Given:
t' = 5 years
distance of the planet from the earth, d = 10 light years = 10 c
Solution:
(a) Distance travelled in a round trip, d' = 2d = 20 c = L'
Now, using Length contraction formula of relativity theory:
(1)
time taken = 5 years
We know that :
time =
5 = (2)
Dividing eqn (1) by v on both the sides and substituting eqn (2) in eqn (1):
Squaring both the sides and Solving above eqution, we get:
v = 0.97 c
(b) Time observed from Earth:
Using time dilation:
Solving the above eqn:
t'' = 20.56 years
Answer:
λ = 102.78 nm
This radiation is in the UV range,
Explanation:
Bohr's atomic model for the hydrogen atom states that the energy is
E = - 13.606 / n²
where 13.606 eV is the ground state energy and n is an integer
an atom transition is the jump of an electron from an initial state to a final state of lesser emergy
ΔE = 13.606 (1 / - 1 / n_{i}^{2})
the so-called Lyman series occurs when the final state nf = 1, so the second line occurs when ni = 3, let's calculate the energy of the emitted photon
DE = 13.606 (1/1 - 1/3²)
DE = 12.094 eV
let's reduce the energy to the SI system
DE = 12.094 eV (1.6 10⁻¹⁹ J / 1 ev) = 10.35 10⁻¹⁹ J
let's find the wavelength is this energy, let's use Planck's equation to find the frequency
E = h f
f = E / h
f = 19.35 10⁻¹⁹ / 6.63 10⁻³⁴
f = 2.9186 10¹⁵ Hz
now we can look up the wavelength
c = λ f
λ = c / f
λ = 3 10⁸ / 2.9186 10¹⁵
λ = 1.0278 10⁻⁷ m
let's reduce to nm
λ = 102.78 nm
This radiation is in the UV range, which occurs for wavelengths less than 400 nm.