Answer:
a) λ = 121.5 nm
, b) 102.6, 97, 91.1 nm
Explanation:
Bohr's model describes the energy of the hydrogen atom
= k² e² / 2m (1 / n²)
A transition occurs when the electron passes from n level to a lower one
- = k² e² / 2m (1 / ² - 1 / ²)
Planck's relationship is
E = h f = h c / lam
hc /λ = k² e²/ 2m(1 / ² - 1 / ²)
1 / λ = [k² e² / 2m h c] (1 / ² - 1 / ²)
1 /λ = Ry] (1 / ² - 1 / ²)
a) the first element of the series occurs for = 2
1 / λ = 1.097 10⁷ (1- 1/2²)
1 / λ = 1.097 10⁷ (1- 0.25)
1 / λ = 0.82275 10⁷
λ = 1.215 10⁻⁷ m
λ = 1,215 10⁻⁷ m (10⁹nm / m)
λ = 121.5 nm
b) the next elements of the series occur to
1 /λ λ (10-7m) λ (nm)
3 1 1,097 10⁷ (1-1 / 9) 1,0255 102.6
4 1 1,097 10⁷ (1-1 / 16) 0.9723 97.2
∞ 1 1,097 10⁷ (1 - 0) 0.91158 91.1
Tan = opposite/adjacent
= 20/15
=4/3
A) Using:
2as = v² - u², where v will be 0 at max height
s = -(160)² / 2 x -32.174
s = 397.8 ft
b) Using:
s = ut + 1/2 at²
256 = 160t - 16.1t²
solving for t,
t = 2.0, t = 7.9
Now, v = u + at, for both times:
v(2) = 160 - 32.174(2)
v(2) = 95.7 ft/sec on the way up
v(7.9) = 160 - 32.174(7.9)
v(7.9) = -94.3 ft/sec; 94.3 ft/sec on the way down
c) -32.174 ft/s², which is the acceleration due to gravity.
d) s = 0
0 = 160t - 1/2 x 32.174t²
t = 9.94 seconds