2, (a) The Heisenberg Uncertainty Principle (HUP) can be expressed as, (i) Defin
ID: 693365 • Letter: 2
Question
2, (a) The Heisenberg Uncertainty Principle (HUP) can be expressed as, (i) Define all the terms in the expression. (ii) Explain, with reference to the expression, what you understand by tbe HUP. (5) (iii) Suppose the speed of a projectile of mass 1.0 g is known to within 1 x 10 ms Calculate the minimum uncertainty in its position. (iv) If an electron has a similar uncertainty in speed as in (ii) above, calculate the (v) Comment on the results obtained in (ii) and (iv) above. minimum uncertainty in its position. (b) Two hydrogen atoms, each with wavefunction Vi, are allowed to interact. (i) Write expressions for the resulting wavefunctions when both originl (ii) Derive the intensity of the resulting wavefunctions of the two cases (ii) What is the significance of the solutions in ii) above, with respect to the wavefunctions are positive and when one is positive and the other is negative. in i) above. interaction of two H-atoms to form a molecule of H2 (2)Explanation / Answer
2)
a. q = uncertainty in position.
v = uncertainty in velocity.
m = mass of moving object/particle.
h= Planck's constant = 6.636*10^-34 J/s.
= 3.14
b)
HUP states that it is impossible to find exact position and velocity of a microscopically moving object with accuracy.And according to the expression the product of q * v is always greater than or equal to (h/4).
c)
In this problem we have to find minimum q = uncertainty in position.
v = 1*10^-6 m/s.
m = 1.0 *10^-3 Kg
h= Planck's constant = 6.636*10^-34 J/s.
= 3.14
q * v = h/4m
q = h/4mv = (6.636*10^-34)/(4*3.14*1*10^-3*1*10^-6)
= 0.528 *10^-25 m/s = 5.28 *10^-26 m/s
d)
For an electron
v = 1*10^-6 m/s.
m = 9.1 * 10^-31Kg
h= Planck's constant = 6.636*10^-34 J/s.
= 3.14
q * v = h/4m
q = h/4mv = (6.636*10^-34)/(4*3.14*9.1*10^-31*1*10^-6)
= 0.0581 *10^3m/s = 5.81*10 m/s
e)
By analyzing above problems it is sure that , this principle holds for microscopic particles only and is negligible for macroscopic objects.
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