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Question: The wavelength of a photon in nm having energy of \( 3.083\times {{10}^{12}}J \) is approximately?...

The wavelength of a photon in nm having energy of 3.083×1012J3.083\times {{10}^{12}}J is approximately?

Explanation

Solution

The wavelength of a periodic wave is its spatial period, or the distance over which the wave's form repeats. It's the distance between two adjacent corresponding points of the same phase on the wave, such two adjacent crests, troughs, or zero crossings, and it's a feature of both travelling and standing waves, as well as other spatial wave patterns.
E=hcλE=\dfrac{hc}{\lambda }
E = energy
H = planck's constant
C = speed of light
λ\lambda = wavelength.

Complete answer:
The energy carried by a single photon is referred to as photon energy. The photon's electromagnetic frequency is directly proportional to the amount of energy it contains, and hence the wavelength is inversely proportional. The greater the frequency of a photon, the more energy it has. In other words, the longer the wavelength of a photon, the lower its energy.
The energy of a photon is the frequency multiplied by the Planck constant; E=hfE=h f and the wavelength of a wave is its speed divided by its frequency;
v=fλ⇒f=vλv=f \lambda \Rightarrow f=\dfrac{v}{\lambda} ,
so its energy, E=hvλ.E=\dfrac{h v}{\lambda} .
This rearranges to λ=hvE\lambda=\dfrac{h v}{E} , where hh is the Planck constant, vv is the speed of light, and EE is the energy of the photon
∴λ=6.63⋅10−34⋅3.0⋅1083.083⋅1012=6.4515⋅10−38 m=6.4515⋅10−29 nm\therefore \lambda =\dfrac{6.63\cdot {{10}^{-34}}\cdot 3.0\cdot {{10}^{8}}}{3.083\cdot {{10}^{12}}}=6.4515\cdot {{10}^{-38}}~\text{m}=6.4515\cdot {{10}^{-29}}~\text{nm}
I guess that you meant to write 3.083⋅10−123.083 \cdot 10^{-12} not 3.083⋅10123.083 \cdot 10^{12} , seeing as gamma rays have a wavelength of ∼10−11m\sim 10^{-11} m , which is ∼10−18\sim 10^{-18} times larger.
If E=3.083⋅10−12JE=3.083 \cdot 10^{-12} J , using the same method, it would give a wavelength of 6.4515⋅10−5nm6.4515 \cdot 10^{-5} n m , which is a reasonable value for electromagnetic waves.

Note:
Energy is the quantitative quality that must be supplied to a body or physical system in order to perform work on it or to heat it, according to physics. Energy is a conserved quantity, meaning it may be transformed in form but not generated or destroyed, according to the rule of conservation of energy. The joule is the energy supplied to an item by the effort of moving it a distance of one metre against a force of one newton, as defined by the International System of Units (SI).