Please help me with four questions below, it would help me out a lot if you can
ID: 1040422 • Letter: P
Question
Please help me with four questions below, it would help me out a lot if you can do all . Please..Use the References to access important values if needed for this question. pes pts Zreq ots 2req Compare the de Broglie wavelength of a proton moving at 1.30 107 miles per hour (5.81 10* m/s) to that of a baseball moving at 90.0 miles per hour (40.2 m/s) and a golf ball with a speed of 70.0 miles per hour (31.3 m/s). pts 2req pts 2req Which region of the electromagnetic spectrum are each of these wavelengths near? A. Ultraviolet 108 to 107 meters 1011 to 108 meters 1016 to 1011 meters 1020 meters. Cannot detect wave-like ots 2req X-ray Gamma ray Smaller than B. pts 2req pts 2req pts 2req pts 2req pts 2req pts 2req C. properties. Only particle-like behavior will be observable D. Mass Velocity Wavelength (kgi Particle Region (m/s) proton 1.67175.81 106 baseball golf ball 31.3 0.140 40.2 Submit Answer Retry Entire Group 4more group attempts remaining
Explanation / Answer
de Broglie equation is expressed
? = h/p
= h / (m v)
Where
? stands for the wavelength of the particle
h stands for Planck's Constant = 6.626 x 10-34 m2 kg s-1
p stands for the momentum of the particle
m stands for the mass of the particle
v stands for the velocity of the particle
Protron:
? = h / (m v)
= (6.626 x 10-34 m2 kg s-1) / [(1.67 x 10-27 Kg) x (8.81 x 106 m s-1)]
= 4.50 x 10-14 m
So, region is Gamma ray (option C)
Baseball:
? = h / (m v)
= (6.626 x 10-34 m2 kg s-1) / [(0.104 Kg) x (40.2 m s-1)]
= 1.58 x 10-34 m
So, region is Smaller than (option D)
Golfball:
? = h / (m v)
= (6.626 x 10-34 m2 kg s-1) / [(4.50 x 10-2 Kg) x (31.3 m s-1)]
= 4.92 x 10-37 m
So, region is Smaller than (option D)
alpha particle:
? = h / (m v)
= (6.626 x 10-34 m2 kg s-1) / [(6.64 x 10-27 Kg) x (1.52 x 107 m s-1)]
= 6.57 x 10-15 m
So, region is Gamma ray (option C)
Energy of an electron in the n = 4 level of hydrogen is expressed as
E = -13.6 eV / n2
= -13.6 eV / (4)2
= -13.6 eV / 16
= - 0.85 eV
= - 0.85 x (1.60218x 10-19) J
= - 1.36x 10-19 J
First calculate the wavelength using the Rydberg equation
1/? = Rh(1/n12 - 1/n22)
= (1.094 x 107) x ( 1/52 - 1/62)
= (1.094 x 107) x (0.012)
= 131280 m-1
We know E = h ?
where ? is frequency and
h is the Planck constant. h is 6.626 x 10-34 kg.m2 s-1
There is a relationship between wavelength and frequency as
c = ??
or ? = c/?
= (3.0 x 108 m s-1) x (131280 m-1)
= 3.94 x 1013 s-1
Therefore
E = (6.626 x 10-34 J s-1) x (3.94 x 1013 s-1)
= 2.62 x 10-20 J