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Calculate the wavelength of light that corresponds to the radiation that is given off during the transition of an electron from the n = 5 to n = 2 state of the hydrogen atom.
- a)434 nm
- b)275 nm
- c)305 nm
- d)183 nm
Correct answer is option 'A'. Can you explain this answer?
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Calculate the wavelength of light that corresponds to the radiation th...
1/wavelength =RH x z2 x (1/22-1/52) =109677 x 1 x (1/4-1/25) =109677 x 21/100 =2303.2m wavelength=1/2303.2m =1/2303.2 x 107nm =434.1nm~434nm
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Calculate the wavelength of light that corresponds to the radiation th...
To determine the wavelength of light corresponding to the transition of an electron from the n = 5 to n = 2 state of the hydrogen atom, we can use the Rydberg formula. The Rydberg formula relates the wavelengths of the spectral lines emitted by hydrogen to the energy levels of the electron.
The formula is given by:
1/λ = R * ((1/n1^2) - (1/n2^2))
Where:
- λ represents the wavelength of light
- R is the Rydberg constant (approximately 1.097 x 10^7 m^-1)
- n1 and n2 are the initial and final energy levels of the electron
Substituting n1 = 5 and n2 = 2 into the formula:
1/λ = R * ((1/5^2) - (1/2^2))
1/λ = R * ((1/25) - (1/4))
1/λ = R * ((4 - 25)/100)
1/λ = R * (-21/100)
1/λ = - R * (21/100)
To find the wavelength, we need to take the reciprocal of both sides of the equation:
λ = -100/(21R)
Since the answer choices are given in nanometers (nm), we need to convert the wavelength from meters to nanometers:
1 meter = 1 x 10^9 nanometers
Substituting the value of R into the equation and performing the calculation:
λ = -100/(21 * 1.097 x 10^7) * 10^9
λ = -100/(21 * 1.097 x 10^-2)
λ = -100/(21 * 0.01097)
λ = -100/0.23037
λ ≈ 434 nm
Therefore, the wavelength of light corresponding to the transition of an electron from the n = 5 to n = 2 state of the hydrogen atom is approximately 434 nm, which matches option A.
The formula is given by:
1/λ = R * ((1/n1^2) - (1/n2^2))
Where:
- λ represents the wavelength of light
- R is the Rydberg constant (approximately 1.097 x 10^7 m^-1)
- n1 and n2 are the initial and final energy levels of the electron
Substituting n1 = 5 and n2 = 2 into the formula:
1/λ = R * ((1/5^2) - (1/2^2))
1/λ = R * ((1/25) - (1/4))
1/λ = R * ((4 - 25)/100)
1/λ = R * (-21/100)
1/λ = - R * (21/100)
To find the wavelength, we need to take the reciprocal of both sides of the equation:
λ = -100/(21R)
Since the answer choices are given in nanometers (nm), we need to convert the wavelength from meters to nanometers:
1 meter = 1 x 10^9 nanometers
Substituting the value of R into the equation and performing the calculation:
λ = -100/(21 * 1.097 x 10^7) * 10^9
λ = -100/(21 * 1.097 x 10^-2)
λ = -100/(21 * 0.01097)
λ = -100/0.23037
λ ≈ 434 nm
Therefore, the wavelength of light corresponding to the transition of an electron from the n = 5 to n = 2 state of the hydrogen atom is approximately 434 nm, which matches option A.
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