Federal prosecutors laid out an evidence-packed case in an indictment unsealed on Friday that former President Donald J. Trump had put national security secrets at risk by mishandling classified documents he took from the White House and then schemed to block the government from reclaiming the material.

The 49-page, 38-count indictment said the documents held onto by Mr. Trump included some involving sensitive nuclear programs and others that detailed the country’s potential vulnerabilities to military attack.

In some cases, prosecutors said, he displayed them to people without security clearances and stored them in a haphazard manner at Mar-a-Lago, even stacking a pile of boxes in a bathroom at his private club and residence in Florida.

The indictment included evidence vividly illustrating what prosecutors said was Mr. Trump’s willingness to hide the material from investigators.