A spectral line is emitted when an atom undergoes tranisition between two levels with a difference in energy of 2.4eV.What is the wavelength of the line (a)287nm(b)507angstrome units()377angstrome units(d)518nm
we know that energy in nth level is (hc/lemda),here denote lemda=l
so
E=E1-E2=2.4ev
E=E1-E2=hc/l;
put the value of "h and c"
{1ev=1.6*10^-19j}
2.4*1.6*10^-19 =(6.64*10^-34 *3*10^8)/l
l=5.187*10^-7m=518.7nm
so answer is (d)
Well, I could tell you the wavelength of the line, but first, let me ask you this: Why did the scarecrow win an award? Because he was outstanding in his field!
Now back to the question. To find the wavelength, we can use the equation:
wavelength = (planck's constant * speed of light) / energy difference
Plugging the given values:
wavelength = (6.626 x 10^-34 J.s * 3 x 10^8 m/s) / 2.4 eV
Now, we need to convert the electron volts (eV) energy difference into joules (J):
1 eV = 1.6 x 10^-19 J
So, energy difference in joules = 2.4 eV * 1.6 x 10^-19 J/eV
Now, we can calculate the wavelength:
wavelength = (6.626 x 10^-34 J.s * 3 x 10^8 m/s) / (2.4 eV * 1.6 x 10^-19 J/eV)
After crunching the numbers, we get the wavelength to be approximately 516 nm. So, the closest option is (d) 518 nm.
Why don't scientists trust atoms? Because they make up everything!
To find the wavelength of the spectral line emitted, we can use the equation:
wavelength = hc/E
where:
wavelength is the wavelength of the spectral line,
h is Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light in a vacuum (3.0 x 10^8 m/s),
and E is the energy difference between the two levels.
Given that the energy difference is 2.4 eV, we need to convert it to joules:
1 eV = 1.6 x 10^-19 J
So, the energy difference is:
E = 2.4 eV x (1.6 x 10^-19 J/eV) = 3.84 x 10^-19 J
Now we can substitute the values into the equation to find the wavelength:
wavelength = (6.626 x 10^-34 J·s) x (3.0 x 10^8 m/s) / (3.84 x 10^-19 J)
wavelength ≈ 5.17 x 10^-7 m
To convert the wavelength to angstrom units, we can use the conversion factor:
1 angstrom unit = 1 x 10^-10 m
So, the wavelength, in angstrom units, is approximately:
wavelength ≈ (5.17 x 10^-7 m) x (1 x 10^10 angstrom units/m)
wavelength ≈ 5170 angstrom units
Therefore, the correct answer is option (d) 518 nm.
To calculate the wavelength of the spectral line, we can use the equation:
λ = hc / ΔE
Where:
λ is the wavelength (in meters),
h is the Planck's constant (approximately 6.626 x 10^(-34) J·s),
c is the speed of light (approximately 3.00 x 10^8 m/s),
ΔE is the difference in energy (in joules).
First, we need to convert the energy difference of 2.4 eV into joules:
1 eV = 1.6 x 10^(-19) J
So, ΔE = 2.4 eV x 1.6 x 10^(-19) J/eV = 3.84 x 10^(-19) J
Now we can substitute the values into the equation:
λ = (6.626 x 10^(-34) J·s)(3.00 x 10^8 m/s) / (3.84 x 10^(-19) J)
Calculating this, we find that the wavelength is approximately 5.17 x 10^(-7) meters or 517 nm.
Therefore, the correct answer is (d) 518 nm.