Structure of Atom
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New answer posted
4 months agoContributor-Level 10
Let the threshold wavelength be λ0 nm or λ0 * 10−9 m.
h (ν−ν0) = ½ mv2
hc (1/λ−1/λ0)= ½ mv2
hc [ (1/500*10−9) – (1/ λ0*10−9)] = ½ m (2.55*106)2 . (1)
Similarly,
hc [ (1/450*10−9) – (1/λ0? *10−9? )] = ½? m (4.35*106)2 . (2)
Similarly,
hc [ (1/400*10−9) – (1/λ0? * 10−9? )] = ½? m (5.2 * 106)2 . (3)
Divide equation (2) by (1),
[ (λ0 – 450) /450λ0] x – [500λ0/ (λ0 – 500)] = (4.35/ 2.55)2
(λ0 – 450)/ (λ0 – 500) = 2.61
λ0= 531 nm.
This is the threshold wavelength.
The value of the threshold wavelength is substituted in equation (3).
h *3*108 (1/400*10−9– 1/531*10−9)= ½ *9.1
New answer posted
4 months agoContributor-Level 10
λ1 = 589 nm = 589 x 10-9 m
ν1 = c / λ1 = (3 x 108 ms-1) / (589 x 10-9 m) = 5.0934 x 1014 s-1
λ2 = 589.6 nm = 589.6 x 10-9 m
ν2 = c / λ2 = (3 x 108 ms-1) / (589.6 x 10-9 m) = 5.0882 x 1014 s-1
ΔE = E1 – E2 = h [ν1 – ν2]
= (6.626 x 10-34Js) x [ (5.0934 x 1014 s-1) – (5.0882 x 1014 s-1)
= 3.31 x 10-22 J
New answer posted
4 months agoContributor-Level 10
(i) Energy of photon (E) = hc / λ
= (6.626 * 10-34 Js) x (3 * 108 m s-1) / (4 * 10-7 m) = 4.969 x 10-19 J
Since, 1.6020 * 10-19 J= 1 eV
So, 1 J= (1 eV) / (1.6020 * 10-19 J)
Hence, 4.969 x 10-19 J = (1eV) x (4.969 x 10-19 J) / (1.602 x 10-19 J) = 3.1 eV
(ii) Kinetic energy of emission = Energy – work function
= (3.1 – 2.13) = 0.97 eV
(iii) Kinetic energy of emission = 0.97 eV
=> ½ mv2= 0.97 eV = 0.97 x 1.602 x 10-19 J = 0.97 x 1.602 x 10-19 kg m2 s-2
=> v2 = (2 x 0.97 x 1.602 x 10-19 kg m2 s-2 ) / (9.1 x 10-31 kg) = 0.34 x 1012 m2 s-2
=> v = (0.34 x 1012 m2 s-2)1/2 = 0.583 x 106 ms-1 = 5.83 x 105 ms-1
New answer posted
4 months agoContributor-Level 10
Given: h = 6.626 * 10-34 Js,
c = 3 * 108 m s-1,
λ = 4000 pm = 4000 * 10-12 m = 4 * 10-9 m
Energy of photon (E) = hc / λ
= (6.626 * 10-34 Js) x (3 * 108 m s-1) / (4 * 10-9 m) = 4.969 x 10-17 J
i.e. 4.969 x 10-17 J is the energy of 1 photon
Therefore, 1 J is the energy of photons = 1 / (4.969 x 10-17) = 2.012 x 1016 photons.
New answer posted
4 months agoContributor-Level 10
Wavelength, λ = (3 * 108 ms-1) / (5 * 109 s-1) = 6.0 x 10-2 m
Frequency, ν = 1 / 2.0 * 10-10 s = 5.0 x 109 s-1
Wavenumber, (? ) = 1 / (6.0 x 10-2 m) = 16.66 m-1
New answer posted
4 months agoContributor-Level 10
(i) Energy of photon (E) = hν, where h= Plank's const, ν= Frequency
h= 6.626 * 10-34 J s ; ν = 3 * 1015 Hz = 3 * 1015 s-1
∴ E = (6.626 * 10-34 J s) * (3 * 1015 s-1) = 1.986 * 1018 J
(ii) Energy of photon (E) = hν = hc/λ, where λ= wavelength
h = 6.626 * 10-34 J s ; c = 3 * 108 m s-1 λ= 0.50 Å = 0.5 * 10-10 m.
∴ E = (6.626 * 10-34 J s) * (3 * 108 ms-1) / 0.5 * 10-10 m = 3.98 x 10-15 J.
New question posted
4 months agoNew answer posted
8 months agoContributor-Level 10
Hello,
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All the very best for all of this, and I hope this helps!
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