Adiffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffraction angle of 34.0°. what is the wavelength of the light?

745.59 nm

Explanation:

The diffraction angles when we have a slit divided into parts are obtained by the following equation:

(1)

Where:

is the width of the slit

is the wavelength of the light  

is an integer different from zero

Now, the first-order diffraction angle is given when , hence equation (1) becomes:

(2)

We know:

In addition we are told the diffraction grating has 750 slits per mm, this means:

Solving (2) with the known values we will find :

(3)

(4)

Knowing :

 >>>This is the wavelength of the light, wich corresponds to red.

Answer: a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same sign as the  -4.0  µc charge.======electricstatic force between two point charges  is given by    where k is coulomb's constant,  8.99×10⁹  n·m²/c², q₁ and q₂ are the point charges, and r is the distance between the two point charges.assign positive to q₁let q₁ =  6.0 µc, q₂ = -4.0  µc, q₀ represent the charge at the origin, and q₃ represent this new charge to place.the charge at the origin q₀ would experience the following force f₀₁ from q₁, with r = 6.0 m (note that 1  µc = 10⁻⁶ c)    the force from q₂    the force from q₃    the net force on the origin charge, q₀, has to be zero for no electrostatic forcehaving an equation where k and q₀ can be divided out of the equation will allow us to solve for q₃    isolating:     a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same as the  -4.0  µc charge