How often do very active sunspot and solar flare cycles take place?

Light from a sodium lamp passes through a diffraction grating that has 1000 slits per millimeter. the interference pattern is viewed on a screen 1.000 m behind the grating. the first (m = 1) two bright yellow fringes that are visible are 0.7288 m and 0.7300 m from the central maximum. what are the wavelengths of these two fringes?

(2) (a) you have a simple circuit that consists of only a battery (δvbat=1.5v) and two resistors with resistance r1=10ω and r2=5ω, connected in series with each other. what is the current running through the battery? (b) you re-arrange your circuit so now r2 is attached in parallel to r1 rather than in series. what is the current running through the battery? (c) you add an additional resistor r3=7ω on the same branch as r2. what is the current running through the battery? (d) what is the power dissipated in r3?

An charge with mass m and charge q is emitted from the origin, (x,y)=(0,0). a large, flat screen is located at x=l. there is a target on the screen at y position y(h), where y(h) > 0. in this problem, you will examine two different ways that the charge might hit the target. ignore gravity in this problem. 1.assume that the charge is emitted with velocity v(0) in the positive x direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l. 2.now assume that the charge is emitted with velocity v(0) in the positive y direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive x direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l.