13.38 . Mini Black Holes. Cosmologists have speculated that black holes the size of a proton could have formed during the early days of the Big Bang when the universe began. If we take the diameter of a proton to be 1.0 X 10-15 m, what would be the mass of a mini black hole?

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3. a) Show that the phase velocity of the de Broglie waves of aparticle of mass m and de Broglie wavelength ? is given by .
b) Compare the phase and group velocities of an electron whose deBroglie wavelength is exactly 1x10-13 m.
4. To what voltages must we accelerate electrons (as in an electronmicroscope, for example) if we wish to resolve;
a) a virus of diameter 12 nm , b) an atom of 0.12 nm, c) a protonof diameter 1.2 fm?
5. a) The x-coordinate of an electron is measured with anuncertainty of 0.20 mm. What is the x- component of the electronâsvelocity, vx, if the minimum percentage uncertainty in asimultaneous measurement of vx is 1.0%.
b) Repeat part (a) for a proton. 6. Suppose Fuzzy, a quantummechanical duck, lives in a world in which h = 2? J.s. Fuzzy has amass
of 2.0 kg and is initially known to be within a region 1.0 mwide.
a) What is the minimum uncertainty in his speed? b) Assuming thisuncertainty in speed to prevail for 5.0 s, determine theuncertainty in position after
this time.
7. The seeing ability, or resolution, of radiation is determined byits wavelength. If size of an atom is of the order of 0.1 nm, howfast must an electron travel to have a wavelength small enough toâseeâ an atom?
8. An air rifle is used to shoot 1.0 g particles at 100 m/s througha hole of diameter 2.0 mm. How far from the rifle must an observerbe to see the beam spread by 1.0 cm because of the uncertaintyprinciple? Compare this answer with the diameter of the universe (? 1026 m).

Please solve all of these equations as early as possible.

1 .

(a) The distance to a star ts approximately
4.21 x 10^18 m. If this star were to burn out today, in how many years would we see it

disappear?

( )years

(b) How long does it take sunlight to reach Earth?
( )minutes .

(c) How long does it take for a microwave radar signal to travel from Earth to the Moon and back? (The distance from Earth

to the Moon is 3.84 x 10^5 km }
( )s.

2. Which of the following statements are true regarding electromagnetic waves traveling through a vacuum?
(Select all that apply }.
1.All waves have the same wavelength.

2.All waves have the same frequency

3.All waves travel at 3.00 x 10° m/s

4. The electric and magnetic flelds associated with the waves are perpendicular to each other and to the direction of wave propagation .

5.The speed of the waves depends on their frequency.

3.What are the wavelength ranges for the following?

(a) the AM radio band (540-1600 kHz)

1.maximum wavelength( ) m.

2.minimum wavelength ( ) m.

(b) the FM radio band (88-108 Mhz)

maximum wavelength ( )m.

minimum wavelength ( )m.

4. What are the wavelengths of electromagnetic wave in free space that have the following frequencies?
(a) 2. 00 x 10^19 Hz

( )pm.

(b) 7.50 x 10^9 Hz

( )cm.

5.A diathermy machine used In physiotherapy generates electromagnetic radiation that gives the effect of "deep heat” when absorbed In tissue One assigned frequency for diathermy ts 915. 00 MHz, What is the wavelength of this radiation?

linear mass density ( )m.

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13.38 . Mini Black Holes. Cosmologists have speculated that black holes the size of a proton could have formed during the early days of the Big Bang when the universe began. If we take the diameter of a proton to be 1.0 X 10-15 m, what would be the mass of a mini black hole?

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