What will be the mass and momenteum of radiation having 3.6A a wavelength frequency
Answers
Answer:
3.6 Angstroms is 0.36 nanometers. A wavelength of this size is categorized as an X-ray and is in the range of sizes typical of atoms.
An x-ray, like any photon, has zero rest mass; however it has kinetic energy, which is the energy that can do work. The energy is equal to Planck’s constant (h) times the speed of light (c) divided by the x-ray's wavelength.
Doing the math, 5.5E-16 is the energy in joules. At this scale it is sometimes better to convert joules into electron-volts. Doing this conversion gives an energy of 3,430 eV.
By comparison, a photon of yellow light has an energy of about 2 eV.
X-rays have considerably more energy than visible light but no rest mass.
Sometimes folks want to convert the kinetic energy of a photon into an equivalent mass. It’s reasonable because photons are never at rest. They travel at light speed in empty space.
Using frequency instead of wavelength, the energy is equivalent to hf (because f = c/λ), which in this case we have already established is equal to 5.5E-16 joules, right?
We know from relativity that momentum p times the speed of light c equals the energy hf.
Therefore, it seems apparent that the energy hf divided by the speed of light c equals the momentum p.
Since momentum p is equivalent to mass times velocity—and the velocity is the speed of light c for every photon in the vacuum of space—the equivalent mass m of a photon must equal its energy hf divided by light twice.
Applying this reasoning to the x-ray photon described by your question, we can divide 5.5E-16 joules by the speed of light c twice to determine its equivalent mass of 6.12E-33 kilograms. Converting to electron-volts reveals an equivalent mass of 3,430 eVs.
In other words, mass and energy are equivalent as Einstein said even when we assume that the rest mass of a photon is zero.
Remember always:
E2=(pc)2+(mc2)2 , where p=hf/c and m is the rest mass.
We don’t need mass to calculate the energy of a photon with a rest mass equal to zero. All that’s needed is it frequency or wavelength.
Answer:
Explanation:
→ λ = h / MV
→ M = h / λV
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M --- mass of proton
h --- planck's constant
λ --- Wave length
V --- Velocity
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→ λ = 3.6 A⁰ = 3.6 × 10⁻¹⁰ m
h = 6.626 × 10 ⁻³⁴
V = 3 × 10⁸ m/s
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∴ M = ( 6.626 × 10 ⁻³⁴ ) / [ ( 3.6 × 10⁻¹⁰ ) × ( 3 × 10⁸)]
= 6. 135 × 10⁻³³ kg /
(or)
As we know that,
λ = h/p
→ ; h = plank's constant
= 6.626×10⁻³⁴ J-s
→ p = momentum of proton
= mass× velocity
=m×v
→ ∴λ = h/mv
⇒m = h/λv
v= velocity of light or proton = 3×10⁸ m/s
λ = 3.6 Α° = 3.6×10⁻¹⁰ m
→ substituting the values
→ m= (6.626×10⁻³⁴)/(3.6×10⁻¹⁰×3×10⁸)
= 6.135× 10⁻³³ kg