Planck’s constant h = 6.63 x 10^-34 Js or 4.14 x 10^15 eVs Planck’s constant h = 1.05 x 10^-34 Js or 6.58 x 10^16 eVs Mass of an electron = 9.1 x 10^-31 kg Charge of electron e = 1.6 x 10^-19 C mc^2 for an electron = 0.511 x 10^6 eV hc = 1240 eV-nm c = 3 x 10^8 m/s
The Correct Answer and Explanation is:
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Your list includes various physical constants, but there seems to be some confusion or inconsistency. Let’s clarify and provide the correct values and then offer an explanation of each.
✅ Correct Physical Constants:
- Planck’s constant (h)
- In joule-seconds:
h=6.63×10−34 J\cdotpsh = 6.63 \times 10^{-34} \, \text{J·s}h=6.63×10−34J\cdotps - In electronvolt-seconds:
h=4.14×10−15 eV\cdotpsh = 4.14 \times 10^{-15} \, \text{eV·s}h=4.14×10−15eV\cdotps ✅ - Reduced Planck’s constant (ħ = h/2π):
ℏ=1.05×10−34 J\cdotps\hbar = 1.05 \times 10^{-34} \, \text{J·s}ℏ=1.05×10−34J\cdotps
ℏ=6.58×10−16 eV\cdotps\hbar = 6.58 \times 10^{-16} \, \text{eV·s}ℏ=6.58×10−16eV\cdotps ✅
- In joule-seconds:
- Mass of electron (me)
me=9.1×10−31 kgm_e = 9.1 \times 10^{-31} \, \text{kg}me=9.1×10−31kg ✅ - Charge of electron (e)
e=1.6×10−19 Ce = 1.6 \times 10^{-19} \, \text{C}e=1.6×10−19C ✅ - Rest mass energy of electron (mc²)
mec2=0.511 MeV=0.511×106 eVm_ec^2 = 0.511 \, \text{MeV} = 0.511 \times 10^6 \, \text{eV}mec2=0.511MeV=0.511×106eV ✅ - hc (Planck’s constant × speed of light)
hc=1240 eV\cdotpnmhc = 1240 \, \text{eV·nm}hc=1240eV\cdotpnm ✅ - Speed of light (c)
c=3×108 m/sc = 3 \times 10^8 \, \text{m/s}c=3×108m/s ✅
🧠 Explanation
These constants form the backbone of quantum mechanics and modern physics. Planck’s constant (h) is central to quantum theory, describing the quantization of energy. It shows up in E = hf, where E is energy and f is frequency. The reduced Planck’s constant ℏ\hbarℏ (h/2π) is commonly used in quantum field theory and the Schrödinger equation.
The mass of the electron, a fundamental particle, is used to calculate its kinetic and potential energy in fields, and it’s crucial for atomic structure and behavior.
Electron charge (e) is the elementary charge, representing the smallest unit of electric charge observed in nature. It’s fundamental in electromagnetism and determines the force between charged particles.
The equation E = mc², where c is the speed of light, gives the rest mass energy of particles. For the electron, this value is 0.511 MeV, meaning if an electron and positron annihilate, 0.511 MeV of energy per particle is released.
The product hc = 1240 eV·nm is particularly useful in photon energy calculations:
E=hcλE = \frac{hc}{\lambda}E=λhc
With E in eV and wavelength λ in nm, this form simplifies optical and X-ray calculations.
Finally, the speed of light (c) connects space and time in relativity and is the maximum speed for energy and information transfer.
In summary, these constants are essential for calculations in quantum mechanics, atomic physics, and special relativity. They link mass, energy, charge, and quantum behavior, forming the foundation of our understanding of the physical universe.
