Assume that the double-slit experiment could be carried out with electrons using a slit spacing of b= 10.0 . To be able to observe diffraction, we choose lamda=b , and because diffraction requires reasonably monochromatic radiation, we choose (delta P)/P= 0.0100.

Part A
What electron momentum would give a position uncertainty of 2.47×10−10m?
Part B
What is the ratio of the wavelength and the slit spacing for this momentum?

In order to answer Part A of the question, we need to use the uncertainty principle, which states that there is a fundamental limit to how precisely we can know both the position and momentum of a particle. Mathematically, it can be expressed as: (delta x) * (delta P) >= h/4*pi, where (delta x) represents the uncertainty in position, (delta P) is the uncertainty in momentum, and h is Planck's constant.

We are given the position uncertainty, (delta x), which is 2.47×10^(-10) m. Plugging in the values, we have:

(2.47×10^(-10)) * (delta P) >= h/4*pi

Now, let's rearrange the equation to solve for (delta P):

(delta P) >= (h/4*pi) / (2.47×10^(-10))

Using the value for Planck's constant, h = 6.63×10^(-34) J·s, we can compute the right side of the inequality:

(delta P) >= (6.63×10^(-34) J·s / (4*pi)) / (2.47×10^(-10))

Now, evaluating the expression:

(delta P) >= 5.34×10^(-25) kg·m/s

Hence, the momentum uncertainty, (delta P), is greater than or equal to 5.34×10^(-25) kg·m/s.

Moving on to Part B of the question, we need to find the ratio of the wavelength (lambda) to the slit spacing (b) for this momentum. The wavelength (lambda) can be related to the momentum (P) of a particle through the de Broglie wavelength equation: lambda = h / P.

Now, rearranging the equation to find the ratio of lambda to b:

(lambda) / b = (h / P) / b

Substituting the given values for Planck's constant and momentum:

(lambda) / b = (6.63×10^(-34) J·s) / (5.34×10^(-25) kg·m/s) / (10.0 m)

Simplifying the expression:

(lambda) / b ≈ 1.24×10^(-9) m / m

Hence, the ratio of the wavelength to the slit spacing for this momentum is approximately 1.24×10^(-9) m/m.