What is the right way to narrow down this research question? broad question: how
did the atomic bomb shape the united states' governmental policies?
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in what ways did the united states' governmental policies change after the
atomic bomb was used during world war ii?
why did the united states' governmental policies change as a result of the
dropping of the atomic bomb?
how did the united states' governmental policies change after world war ii?
how did the atomic bomb impact the united states' foreign policy with regard
to nuclear weapons after world war ii?

The correct answer is the last one: How did the atomic bomb impact the United States' foreign policy with regard to nuclear weapons after World War II?

Explanation:

In order to narrow down a research question into what you are really aiming to investigate, the question must have the question words and the elements that are most directly associated with your research objective.

The key elements of the initial question are as it follows: "How did the atomic bomb shape the United States' governmental policies?". The question refers to the atomic bomb, not to its use in World War II but only to its creation, and to the American governmental policies. So it follows that key elements are nuclear weapons and governmental policies.

Therefore it's possible to narrow down the research question without losing its initial goal referring especifically to foreign policy regarding nuclear weapons after the invention of the atomic bomb.