Question

Based on your knowledge of the period, what events could have led to the increase in the number of German and Irish immigrants to the united states between 1840 and 1850?

Answer 1

If you don't already have knowledge of the period, you might look for a timeline of key events in the 19th century.  You'd find a couple things related to this question:
In the German states and elsewhere in Europe in 1848 there were a number of revolution movements, trying to replace old conservative governments. The revolutions had a more liberal flavor (wanting parliaments and such). Some also had a strong nationalist flavor -- in Germany, that meant creating a united Germany.  But the revolutions failed, and many of those who wanted to see change in the German states left and went to the United States.  I live in a town where many of them showed up!
As for Ireland, from 1845-1849 there was a devastating famine.  Ireland had depended on the potato as its chief crop and food source. When a disease struck the potato plants, famine conditions became awful -- and governments did little to help.  Many Irish people left, hoping to find new lives in America.