Answer:
1. λ = 1.4x10⁻¹⁵ m
2. a) n=2, l=1, [tex]m_{l}[/tex]= -1, 0, +1, [tex]m_{s}[/tex] = +/- (1/2)
b) n=3, l=0, [tex]m_{l}[/tex]= 0, [tex]m_{s}[/tex] = +/- (1/2)
c) n=5, l=2, [tex]m_{l}[/tex]= -2, -1, 0, +1, +2, [tex]m_{s}[/tex] = +/- (1/2)
Explanation:
1. The proton's wavelength can be found using the Broglie equation:
[tex] \lambda = \frac{h}{mv} [/tex]
Where:
h: is the Planck's constant = 6.62x10⁻³⁴ J.s
m: is the proton's mass = 1.673x10⁻²⁴ g = 1.673x10⁻²⁷ kg
v: is the speed of the proton = 2.90x10⁸ m/s
The wavelength is:
[tex] \lambda = \frac{h}{mv} = \frac{6.62 \cdot 10^{-34} J.s}{1.673 \cdot 10 ^{-27} kg*2.90 \cdot 10^{8} m/s} = 1.4 \cdot 10^{-15} m [/tex]
2. a) 2p
We have:
n: principal quantum number = 2
l: angular momentum quantum number = 1 (since is "p")
[tex]m_{l}[/tex]: magnetic quantum number = {-l,... 0 ... +l}
Since l = 1 → [tex]m_{l} = -1, 0, +1[/tex]
[tex]m_{s}[/tex]: is the spin quantum number = +/- (1/2)
b) 3s:
n = 3
l = 0 (since is "s")
[tex]m_{l}[/tex] = 0
[tex]m_{s}[/tex] = +/- (1/2)
c) 5d:
n = 5
l = 2 (since is "d")
[tex]m_{l}[/tex] = -2, -1, 0, +1, +2
[tex]m_{s}[/tex] = +/- (1/2)
I hope it helps you!
Answer:
(1) The wavelength of the proton is 1.366 x 10⁻¹⁵ m
(2) 2p( l = 1, ml = -1,0,+1)
3s( n = 3, l = 0, ml = 0)
5d ( l = 2, ml = -2,-1,0,+1,+2)
Explanation:
Given;
mass of the proton; m = 1.673 x 10⁻²⁴ g = 1.673 x 10⁻²⁷ kg
velocity of the proton, v = 2.9 x 10⁸ m/s
The wavelength of the proton is calculated by applying De Broglie's equation;
[tex]\lambda = \frac{h}{mv}[/tex]
where;
h is Planck's constant = 6.626 x 10⁻³⁴ J/s
Substitute the given values and solve for wavelength of the proton;
[tex]\lambda = \frac{h}{mv}\\\\ \lambda = \frac{(6.626*10^{-34})}{(1.673*10^{-27})(2.9*10^8)}\\\\\lambda = 1.366 *10^{-15} \ m[/tex]
(2) the values for the quantum numbers associated with the following orbitals is given by;
n, which represents Principal Quantum number
[tex]l,[/tex] which represents Azimuthal Quantum number
[tex]m_l,[/tex] which represents Magnetic Quantum number
(a) 2p (number of orbital = 3):
[tex]l= 1\\m_l = -1,0,+1[/tex]
(b) 3s (number of orbital = 1):
[tex]n= 3\\l=0\\m_l= 0[/tex]
(c) 5d (number of orbital = 5)
[tex]l=2\\m_l = 2, -1, 0, +1, +2[/tex]
