Fake news on social media has large, negative implications for society. However, little is known about what linguistic cues make people fall for fake news and, hence, how to design effective countermeasures for social media. In this study, we seek to understand which linguistic cues make people fall for fake news. Linguistic cues (e.g., adverbs, personal pronouns, positive emotion words, negative emotion words) are important characteristics of any text and also affect how people process real vs. fake news. Specifically, we compare the role of linguistic cues across both cognitive processing (related to careful thinking) and affective processing (related to unconscious automatic evaluations). To this end, we performed a within-subject experiment where we collected neurophysiological measurements of 42 subjects while these read a sample of 40 real and fake news articles. During our experiment, we measured cognitive processing through eye fixations, and affective processing in situ through heart rate variability. We find that users engage more in cognitive processing for longer fake news articles, while affective processing is more pronounced for fake news written in analytic words. To the best of our knowledge, this is the first work studying the role of linguistic cues in fake news processing. Altogether, our findings have important implications for designing online platforms that encourage users to engage in careful thinking and thus prevent them from falling for fake news.